Finding aid for the Atle Selberg Papers
FAC.SELBERG

Summary Information

Repository
Shelby White and Leon Levy Archives Center
Creator
Selberg, Atle
Title
Atle Selberg papers
ID
FAC.SELBERG
Date
circa 1920-2007
Extent
18.0 linear feet (10 feet available for research as of August 2012)
Language
English
Language of Materials note
Materials in English and Norwegian.

Preferred Citation note

The suggested citation for the material is "[item], Atle Selberg papers, Box [box number], From the Shelby White and Leon Levy Archives Center of the Institute for Advanced Study, Princeton, NJ, USA."

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Biographical/Historical note

Widely regarded as one of the world’s greatest analytic number theorists, Norwegian mathematician Atle Selberg was appointed Professor in the School of Mathematics at the Institute for Advanced Study in 1951. He was Professor Emeritus from 1987 until his death in 2007.

Throughout a career spanning more than six decades, Selberg made significant contributions to modular forms, Riemann and other zeta functions, analytic number theory, sieve methods, discrete groups, and trace formula. The impact of his work is evident from the many mathematical terms that bear his name: the Selberg Trace Formula, the Selberg Sieve, the Selberg Integral, the Selberg Class, the Rankin-Selberg L-Function, the Selberg Eigenvalue Conjecture, and the Selberg Zeta Function.

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Arrangement note

The collection is arranged into four series: Professional Correspondence; Institute Business; Mathematical Papers; and Photographs.

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Administrative Information

Publication Information

Shelby White and Leon Levy Archives Center

Historical Studies-Social Science Library
Einstein Drive
Princeton
NJ, 08540
609-734-8375
archives@ias.edu

Conditions Governing Access note

All material listed is available for research. Additional material is still closed pending review per the donor agreement.

Custodial History note

The bulk of papers were retrieved from Atle Selberg's home and office at the Institute by Dennis Hejhal after Selberg's death in 2007. They were formally donated to the Institute by Betty Compton Selberg in 2009, with the condition that the mathematical papers be reviewed by Dennis Hejhal and Peter Sarnak prior to making them public. Seven cartons of mathematical papers were cleared for public access in July 2012. Approximately eight feet of papers still await review as of this writing in August 2012. A small amount of additional material was donated by Betty Compton Selberg in 2012.

Processing Information note

Two boxes of professional correspondence and Institute administrative materials were formally transferred to the Archives and processed in 2009. As there was little organization originally, materials were rehoused in standard archival containers and arranged alphabetically by correspondent or chronologically by year. The Photographs series was processed in 2012.

Seven cartons of the mathematical papers were cleared for public access in 2012. Physical processing was done by Dennis Hejhal between 2007-2012, during the process of clearing the materials for public access. No further physical processing or item-level description was undertaken by the Archives staff at that time.

Existence and Location of Copies note

The School of Mathematics at the Institute for Advanced Study maintains a website that features digital copies of some of the documents in the Mathematical Papers series at http://publications.ias.edu/selberg. The entirety of the Photographs series is available online at http://cdm.itg.ias.edu/cdm/search/collection/coll3/searchterm/Atle Selberg papers.

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Collection Inventory

Professional Correspondence 1951-2006   1.25 linear feet

Scope and Contents note

The Professional Correspondence series contains incoming and some outgoing correspondence between Atle Selberg and professional colleagues. There is one folder of material related to members of his family.
Box

Annals 1958-1965 

 1

Bateman, P.T. 1952-1975 

 1

Brauer, Richard 1961 

 1

Carleson, Lennart 1972-1981 

 1

Chandrasekharan, K. 1960-1993 

 1

Chowla, Sarvadaman 1952-1972 

 1

Chudnovsky, G. 1977-1979 

 1

Cohen, Eckford 1951-1961 

 1

Cohen, Paul 1964 

 1

Delange, H. 1975 

 1

Doi, Koji 1962-1966 

 1

Editorial - Miscellaneous 1955-2006 

 1

Erdös, Paul 1975 

 1

Evans, Ron 1980 

 1

Fried, Michael 1968 

 1

Friedlander, John 1976-2001 

 1

Good, Anton 1984 

 1

Hafner, James 1979-1983 

 1

Hedlund, G.A. 1962 

 1

Hejhal, Dennis 1977-2000 

 1

Hensley, Douglas 1977 

 1

Huang-Miller, Julia 1982-1984 

 1

Invitations - Miscellaneous 1961-2006 

 1

Kaplan, Lewis D. undated 

 1

Langlands, Robert 1961-1966 

 1

Maaps, Hans 1969-1972 

 1

Montgomery, Deane undated 

 1

Montgomery, Hugh 1971-1975 

 1

Mozzochi, C.J. 1988 

 1

Murthy, T.S. Bhanu 1965-1971 

 1

Niebur, Doug 1972-1974 

 2

Norton, Karl 1973-1974 

 2

Novodvorsky, Mark 1975 

 2

Personal 1964-1997 

 2

Protter, M.H. 1962-1965 

 2

Ramachandra, K. 1975-1976 

 2

Ramanathan, K.G. 1961-1982 

 2

Reddy, A.R. 1977-1981 

 2

Roelcke, Walter 1954-1970 

 2

Sarnak, Peter 1983-2001 

 2

Soundarajan, Kaman 2002 

 2

Strömgren, Bengt 1963 

 2

Summer Institutes 1964-1969 

 2

Symposium in Honor of Marston Morse - Differential Topology (1962) 1962-1964 

 2

Terras, Audrey 1970-1985 

 2

Tsang, Kai-Man 1985-1995 

 2

Weinstein, Leonard 1987 and undated 

 2

Whiteman, Albert 1951-1966 

 2

Wolf Prize 1978 

 2

Family 

General note

Includes clippings, memorial programs, photocopies of photographs (and one original) related to members of Selberg's family.

 2

Miscellaneous Chronological 
Box

1951 

 2

1952 

 2

1957 

 2

1958 

 2

1959 

 2

1960 

 2

1961 

 2

1962 

 2

1963 

 2

1964 

 2

1965 

 2

1966 

 2

1967 

 2

1968 

 2

1969 

 2

1970 

 3

1971 

 3

1972 

 3

1973 

 3

1974 

 3

1975 

 3

1976 

 3

1977 

 3

1979 

 3

1981 

 3

1984 

 3

1985 

 3

1986 

 3

1987 

 3

1988 

 3

1989 

 3

1990 

 3

1993 

 3

1996 

 3

1997 

 3

1999 

 3

2002 

 3

2004 

 3

2005 

 3

undated 

 3

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Institute Business 1951-2000   1.25 linear feet

Scope and Contents note

The Institute Business series contains correspondence, reports, memos, and other documentation related to Selberg's administrative activities as an Institute Faculty member.
Box

1951 

 3

1952 

 3

1953 

 3

1954 

 3

1955 

 3

1956 

 3

1957 

 3

1958 

 3

1959 

 3

1960 

 4

1961 

 4

1962 (2 folders) 

 4

1963 

 4

1964 

 4

1965 

 4

1966 

 4

1967 

 4

1968 

 5

1969 

 5

1970 

 5

1971 

 5

1972 

 5

1973 

 5

1974 

 5

1975 

 5

1976 

 5

1978 

 5

1979 

 5

1980 

 5

1981 

 5

1982 

 5

1983 

 5

1985 

 5

1987 

 5

1988 

 5

2000 

 5

undated 

 5

Kurt Gödel papers 1979-1982 

 5

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Mathematical Papers 

General note

The seven boxes listed were cleared for public access by Dennis Hejhal and Peter Sarnak in July 2012. Physical processing and description was provided by Dennis Hejhal.

Scope and Contents note

The Mathematical Papers series consists primarily of notes, papers, lectures, and other documentation related to Selberg's mathematical work. It also contains some correspondence, copies of transcripts for interviews with Selberg conducted by Betsy Devine for the Institute's Oral History Project in 1989, published works, and an incomplete set of reprints of Selberg's papers.
Box Envelope

Early Diverse working papers on spectral theory; automorphic forms, including higher dimensional; lecture preparations (some trace formula). likely 1953-1959 

 3 1

5 sheets directly connected to the 1956 Bombay Trace Lecture, pp. 53 (top), 80-81. circa 1956 

 3 2

Draft and working papers for "A new type of zeta functions connected with quadratic forms" (Boulder, 1959). + A nice (Christmas, birthday) sketch in pencil 

 3 3

Some working notes partly tied to the 1954 Gottingen Trace Lectures and to poles of Eisenstein series. 1960-1970 

 3 4

Fragments of lectures dealing especially with symplectic modular forms. (Includes representation of generalized zeta functions in spirit of Riemann's third representation of ζ(s).) See also "Linear operators and automorphic forms" (Bombay 1988). circa 1960-1970 

 3 5

Sparse Fragments on Automorphic Forms and Eisenstein Series in Higher Dimension. probably post-1962 

 3 6

Prelim version of "Sieve methods" (Stony Brook, 1969) 1969 

 3 7

Fragments on sieves, one intermingled with trace formula and spherical functions. probably 1969 or later 

 3 8

Diverse fragments on sieves circa 1969 or a bit later 

 3 9

Lecture draft and preparations on the large sieve circa 1969-1970 

 3 10

Diverse pages: Some on sieves or large sieves, circa 1969-1985. Draft of letter to Halasz, 1985. circa 1969-1985 

 3 11

Draft pages concerning "Remarks on sieves" (Colorado) circa 1972 

 3 12

Three fragments: one for log zeta moments, one for "remarks on multiplicative functions" (1976), one unidentified. circa 1976-1984 

 3 13

Sparse Fragments on sieve theory, automorphic forms, prime geodesics. Possibly for lecture preparations. post 1976 

 3 14

Some lecture preparations, mostly around trace formula. circa 1975-1985 

 3 15

Diverse fragments - zeta, log zeta, sieves, lecture preparations. circa 1980-1989 

 3 16

Diverse tablets on diverse topics with no clear link to publications. post 1969 

 3 17

Diverse working papers with no clear link to publications. pre 1975 

 3 18

Diverse working papers and lecture preparations: zero-density theorems, log [], [], Nevanlinna theory idea, []. circa 1970-1971 

 3 19

Tablet with diverse topics, including one with link to Lemma [] in "Remarks on distribution of poles in Eisenstein series". circa 1976-1977 

 3 20

Diverse fragments, tablets grouped together. circa 1964-1969 

 4 1

Diverse tablets and fragments found grouped together. One tablet contains a draft abstract "On some problems of analytic continuation of Dirichlet series circa 1966-1969 

 4 2

Tablets with diverse fragments, incl. log [] being Gaussian; also some zero-density ideas circa 1968 

 4 3

Two Tablets with diverse fragments, including Beurling-Selberg majorant/minorant functions; some symplectic modular forms; class numbers; and Selberg character sums. late 1960s-1973 

 4 4

Twin Prime List made on computer by Hedi Selberg; A. Selberg's pre-1967 bibliography; xerox copies of some articles read by A.S. 1982-1989 

 4 5

Work from Syracuse University; material on sieves; material on elementary methods in prime number theory, especially for generalized primes; these things may be partially from lectures there; (generalized primes on web). circa 1948 

 4 6A

Some notes made by Audrey Terras based on Atle Selberg's comments to her about differential operators acting on higher-dimensional automorphic forms; remarks on Dirichlet series, too. circa 1969 

 4 7A

Photocopy of one of his father's (Ole M. Selberg) papers. 

 5 1

Assorted mathematical letters (Aubert, Connes, et. al.) and articles. 1986-1996 

 5 2

Carbon copy of typescript for "On discontinuous groups in higher-dimensional symmetric spaces" circa 1960 

 5 3

Atle Selberg Lecture Titles for Tel Aviv 18 July 1991 

 5 4

Fragments. Includes automorphic forms, trace formula SL(2, []), Kloosterman-type zeta function. circa 1975-1985 

 5 5

Fragments and preparations on sieves. circa early 1980s 

 5 6

Preparations and fragments on sieves. Part has emphasis on Y. Brun. Cf. "Lectures on sieves." circa 1979-early 1980s 

 5 7

Draft of "Linear Operators and automorphic forms" and preprint of same. circa 1988 

 5 8

Reprints for "Reflections around the Ramanujan Centenary." circa 1988 

 5 9

Transparencies for a lecture on Ramanujan's formula for p(n). See Collected Works, vol. 1, pp. 701-706. Also earlier envelope. circa 1988 

 5 10

Handwritten draft of Amalfi Lecture. circa 1989 

 5 11

Fragments. Chiefly on sieves. Drafts of letters to Dr. Dawson and about C. Hooley. circa 1980s 

 5 12

Corrected Version of "Remarks on the distribution of poles of Eisenstein series." circa 1990 

 5 13

Fragments. Various topics. One page makes reference to hybrid trace formula (lecture fragment) 1970s-1980s 

 5 14

Some fragments involving trace formula and Rankin-Selberg integral (probably 1980s). Also a self-sketch (1990s?) 1980-1990s 

 5 15

Fragments and scratch. Various topics. Includes some numerical calculations in long hand. 1960s-early 1970s 

 5 16

Fragments. On Automorphic forms in higher-dimensions and sieves. 

 5 17

Fragments. Assorted tablets including a mix of automorphic forms, Rankin-Selberg, prime geodesic theorem, sieves, Selberg integral. 

 5 18

A few pages of calculation associated with the Selberg transform on upper half-plane 

 5 19

Diverse working papers; some trace formulas; some sieves; possibly while at Stanford University; also, draft of letter about lattice point problems, and Stanford, possibly to K.S. Chandrasekharan. probably 1980s 

 5 20A

 circa 1987 

 5 21A

 

 5 22A

Drafts of letters of recommendation for James Hafner and Henryk Iwaniec; incomplete; context unclear. 

 5 23A

Assorted work sheets and very preliminary drafts of letters of recommendation; very curious inequality for |Σanbmcl/Δ(m,n,l)|3; draft of letter that appears to be to Werner Fenchel in Copenhagen about the death of Fenchel's wife. probably 1983-1988 

 5 24A

Lecture preparations and fragments dealing with 0-density results for ζ(s); part later than 1965 or so due to exponent pairs; also, a fragment on large sieve and Bessel's inequality. circa 1965 

 5 25A

Diverse working tablets. Many topics. Especially Selberg integral, zeta function, trace formula on SL(2,R). Popular article on primes by Bombieri. circa late 1980s-early 1990s 

 6 1

Folder on Selberg integral; Selberg character sums; draft of a lecture; material from Ron Evans. A few pages on q-series. circa 1980-1989 

 6 2

Diverse Fragments. Some on discontinuous groups, sieve Schwarzian derivative et al, some lecture preparations. post 1980, early 1990s 

 6 3

Diverse fragments - sieves, SL(2,R) trace formula, Beurling function, also non-math. some early 1990s, probably all post 1980 

 6 4

Diverse fragments/tablets. Also lecture preparations on positive proportion for linear combinations; Mathematical correspondence (1991) with Chandrasekharan. 1990-1998 

 6 5

Portion of a mathematical letter from Audrey Terras. Working copy of "Remarks on Sieves" for Collected Works, col. 1. circa 1982-1988 

 6 6

Plot of a Maass wave form by F. Steiner circa 1992-1993 

 6 7

A tablet dealing mainly with generalized Hilbert inequality; goes in same proximity as Box 6 Envelope 4. 

 6 8A

Lecture materials dealing somehow with large sieve and generalized Hilbert inequality; four transparencies; also page with curious Hecke operator zeta function; goes in proximity with Box 6 Envelope 5. 

 6 9A

Original typed copy of "Lectures on Sieves" finalized by Dottie Phares. Also part of handwritten manuscript. 

 7 1

Xerox of "famous" Jan 24, 1973 letter to Minot Morgan @ IAS about "not recalling my own remarks. January 24, 1973 

 7 2

Materials concerning 1997 visit to Uppsala University. Also related copy of Selberg family entry in Norske Biografisk Leksikon (1958) sent by D. Hejhal at approximately same time. 

 7 3

Handwritten draft and then carbon copy of typescript for "Discontinuous groups and harmonic analysis" (1962). Also Atle Selberg's bibliography up to 1981. 

 7 4

Handwritten draft of "Recent developments in the theory of discontinuous groups of motions of symmetric spaces" (1968). 

 7 5

Typescripts for "Sieve Methods" (Stony Brook lectures, 1969) and "Remarks on Sieves" (1972). 

 7 6

Abstracts for 1955 Research Conference on the Theory of Numbers (Pasadena). Two copies, mimeographed. 

 7 7

Abstracts of papers presented at the International Colloquium on Zeta Functions, 1956, Bombay Mimeographed. (pp. 1-42 only.) 

 7 8

Galley proof material for "On the estimation of Fourier coefficients of modular forms" (1965), "Remarks on multiplicative functions" (1976), and Collected Papers, vol 2. 1991. 

 7 9

Handwritten draft of the appendix to "Reflections around the Ramanujan centenary." 1987-1988 

 7 10

Notes outlining the work of E. Bombieri 

 7 11

Carbon Copy of a typescript "Harish Chandra's work on group-theory (translation of a report by R. Godement)", 20pp. - given to Beurling and Selberg. 

 7 12

Carbon copy of a Doklady translation, Pyatetski-Shapiro, "Discrete Subgroups of analytic automorphisms of a polycylinder and automorphic forms" (1959). Page 6 missing 

 7 13

Working materials/drafts relating to publication of Axel Thue's Selected Papers. Includes letters from C. L. Siegel and S. Selberg. circa 1974 

 7 14

Colloquium lecture notes on zeros of zeta, after Levinson's 1974 result + a copy of Levinson's paper. Also: Tom Apostol's poem "Where are the zeros of zeta of s?" 

 7 15

Some Reprints and preprints of special interest to A.S: S. Selberg, "Ernst Jacobsthal", 1965; S. Selberg, "einige neuere Ergebnisse in der analytischen Zahlentheorie", circa 1974; V. Vrun, "Music and ternary continued fractions", 1950. A. Weil, "Sur les origines de la geometrie algebrique", 1981. G. Kreisel, "Kurt Gödel, 1906-1978", Royal Society Memoirs, 1980. P. Heegaard, "Geometri som bifag", Oslo 1925 (given to A.S.'s father). H. Montgomery, "Vaughan's simple proof of Vinogradov's lemma." K. Aomoto, Jacobi polynomials associated with Selberg integrals", circa 1985 

 7 16

Some Correspondence and Mathematical developments associated with S. Chowla; on J(t)=rational and on the Schmidt-Stepanov proof. 

 7 17

Some fragments on sieves; higher-dimensional automorphy factors; some sort of Beurling-Selberg type function; sgn S(t) 

 7 18

Mathematical correspondence with E. Bombieri on large sieve circa 1969 

 7 19

Fragments on 2-dim value distribution, symplectic automorphic forms. post-1970 

 7 20

Fragments on log [] (s) and [] (s), moments and value distribution; also on symplectic groups and zeta-functions, Selberg integrals, Selberg character sums. 

 7 21

Fragments of handwritten lecture notes on trace formulas either close to 1956 bombay paper or 1954 Göttingen lectures. post-1970 

 7 22

Referee's report and comments on a paper of Shimizu: Carbon copy 

 7 23

Curious "proof" of the Riemann Hypothesis (1964). Also correspondence with L. J. Mordell (1969) about Hardy's "A Mathematician's Apology." 1964-1969 

 7 24

3 drafts of a letter to Hans Maass concerning an error that Maass pointed out in the 1962 Congress Paper. Also one [seemingly] related page. 

 7 25

List of mathematical papers by H. L Selberg, drawn up by Atle Selberg 

 7 26

History of the School of Mathematics, 1980; also a working paper for that report. 

 7 27

Fragment of Beersheva lecture on large sieve; also of a general survey on sieves. Several additional pages on sieves. post-1973 

 7 28

Tagungsbericht March 1968 Oberwohlfach (A.S. participated). Also Erevan meeting scientific program (1965) and Helsinki hotel record (August 1957). 

 7 29

Early mathematical correspondence (and papers) from D. A. Hejhal (1973, 1974). Also postcard from Durham Meeting (1983) signed by many participants. 

 7 30

Mathematical correspondence with P. J. Myrberg (1957), R. Breusch (1999), S. Helgason (1963), S. J. Patterson (1984), and Kai-man Tsang (1998). Also pertaining to Steven Gaal (1969) and London Math Society (1985). Possibly also Takahiro Shiota (1988). 

 7 31

Lecture on Gram's law; these pages scanned. circa 1947 

 7 32A

Notes on the circle problem; the R+ result; these pages scanned and on web. 

 7 33A

Working notes and lecture prepartion on Gaussians and L-function from Stanford University course; xerox copy of Jay Jorgenson's class notes. circa 1985 

 7 34A

Scraps on Selberg trace formula for Hn; nice formula for Z(s). 1950s and undated 

 7 35A

Some scraps related to: Gaussians for L-functions, or item #35 (section 7.5) in bibliography, how now brown cow?. 

 7 36A

Letter from John Nash to Selberg concerning π(x)-∞Σn=1 li(x 1/n )/n. early 1960s 

 7 37A

Some scraps on something related to the Loewner differential equation in complex analysis; some strange analysis about a polynomial equaltion P(zζ1,...,zζn)=0; possibly for rigidity/arithmeticity. 

 7 38A

Working notes for part of item #35 (L-function aspect of section 7.5) in bibliography and an old lecture involving discrete subgroups; scanned materials. probably 1960s 

 7 39A

Working notes, fragments, on generalized Hilbert-type inequality; cf. work of Hugh Montgomery. 

 7 40A

Selberg's copy of "Report of The Institute In The Theory of Numbers", University of Colorado, Boulder, June 21-July 17 1959; Selberg's article (p. 1-7): "Some problems concerning discontinuous groups of isometries in higher dimensional symmetric spaces." 1959 

 8 1

Materials prepared by Selberg about Deane Montgomery for Notices of the American Mathematical Society and for the memorial service held for Montgomery at the Institute for Advanced Study. 

 8 2

International Congress of Mathematicians address given by Harald Bohr about Selberg's and Laurent Schwartz's Fields Medals. 1950 

 8 3

Mimeographed preprint of Selberg and Chowla, "On Epstein's Zeta-function" (40 pp.); item #34 in bibliography. 

 8 4

Program from 70th birthday celebration, Oslo, June 1987 (2 copies); also copy of portrait photo - apparently used in the Oslo newspaper. 

 8 5

Volume of Skrifter det Norske Videnskaps-Akademi, Oslo, containing Selberg's paper on Dirichlet L-functions. 1946 

 8 6

Important mathematical clippings saved by Selberg: reprint from Viggo Brun about Niels H. Abel (Crelle), Viggo Brun in memoriam by S. Selberg, articles about Viggo Brun (August 1978), article by Brun on sieves, Carl L. Siegel's paper on the Riemann Nachlass, reprint about Caspar Wessel and complex numbers by Viggo Brun. 

 8 7

About a dozen newspaper clipping from around 1948-1949, in Norwegian, about prime number theorem proof - possibly sent to Selberg by his family, and including the "Dagens navn" rotogravure piece and also an article from his mother's 90th birthday; also, clipping about MacArthur Prize (August 13, 1979). 

 8 8

Annotated and unused dedicated reprints (17); probably used by Selberg. 

 8 9

Annotated and unused dedicated reprints (7) and one page "automorphic functions and integral operators." 

 8 10

Very old-looking papers containing Selberg's explication of Titchmarsh, Quarterly Journal of Mathematics 18(1947), "On the zeros of the Riemann zeta function"; may have been used in a lecture given by Selberg. probably 1948 

 9 1

Twelve orderly handwritten pages (working notes) on what seems to be a lecture very similar to 1999 Mathematical Sciences Research Institute; the pages have improved estimates (1)-(2) for integral of |Iκ|2 and |Mκ|2 and lead to a "c/n" result; about two-thirds are in Norwegian; no transparencies for this work were found; these materials have been scanned. 

 9 2

Folder with handwritten lecture preparations and a few initial transparencies for a lecture very similar to Lecture 7 in Hong Kong; handwritten portions of these notes were scanned. 

 9 3

Lecture preparations, incomplete, for what seems to be part of Amalfi talk (or similar) on F'(s)/F(s); these materials were scanned. 

 9 4

Handwritten, clearly incomplete, lecture preparations for a positive proportion talk; tablet with some working notes on material related to log ζ' talk, and extra pages!; tablet with some working notes related to Gaussian value distribution of log ζ. circa 1998 and undated 

 9 5

Material brought from home by Betty Selberg: (A) part of a xerox of transparencies from 1999 Mathematical Sciences Research Institute (MSRI) talk with revisions and augmentations entered by Selberg on it (scanned); (B) a complete xerox of the MSRI transparencies, no revisions; (B1) xerox copy of Hejhal's notes from 1999 MSRI lecture; (C) xerox copy of the typed version of Hong Kong Lecture 7; (D) a pile of material prepared by Dennis Hejhal concerning possible revisions to the 1999 MSRI lecture so as to obtain "c/n", which dates to circa 2005. 

 9 6

Some scraps of a lecture preparation on positive proportion; xerox of transparencies from a hybrid trace formula talk - from Selberg's 1997 visit to Uppsala, and given to him by Dennis Hejhal; xerox of transparencies from positive proportion talk at Uppsala University on 8 September 1998, and sent to Selberg by Dennis Hejhal (scanned). 

 9 7

Reprints of papers 1-20, but #13 and #17 could not be found. 

 10 1

Reprints of papers 21-37, with #29, 35, 37 missing. 

 10 2

Reprints of papers 38-45, but #39, 41, 43, 45 are missing (possibly because none were furnished). 

 10 3

3 reprints not in collected works. (Norwegian) "Minnetale over Professor Viggo Brun" (1979), 15 pp; Normat 37 no. 1 (1989), 2-7; Normat 37 no. 4 (1989), 141-146. 

 10 4

Several Volumes from "Det Norske Videnskaps-Akademi: Oslo".* (a) History II, 1857-1957 [refers to Atle Selberg] (b) Årbok 1965, 1975, 1979, 1991, 1994 [connected with A.S] *=The Norwegian Academy of Science and Letters   6.0 volumes

 10 5

Several Volumes from "Det Kongelige Norske Videnskabers Selskab"*(b) Forhandlinger 2000 [segment about A.S] (a) Forhandlinger 1976, 1978 [connected with A.S.] *=The Royal Norwegian Society of Sciences and Letters   3.0 volumes

 10 6

Street Map of Oslo; Geological map of Oslo area (1952, Det Norske Videnskaps-Akademi i Oslo); Railroad map or Norway (NSB, 1990) 

 10 7

Early corrections to interview by Nils A. Baas and Christian F. Skau; final corrections to inverview by Baas and Skau; binder with the November interview. 2005 

 11 1

Interview by Betsy Devine (1989) (scanned for website); interview material (1999) for the book authored by D. Albers and G. Alexanderson, "Mathematical People: Profiles and Interviews"; old curriculum vitae for Selberg (scanned); Board of Trustee Meeting (October 2005) and meeting agenda; "Music of the Primes: Searching to Solve the Greatest Mysteries in Mathematics" excerpt and "My Brain is Open: The Mathematical Journeys of Paul Erdos" excerpt regarding Erdös-Selberg. 

 11 2

Nils A. Baas - Gunnerus forelesning (February 2000); honorary doctorate promotion - September 1994 - University of Oslo, where Selberg was honored; biographical material on Niels H. Abel (1802-1829) by Christian Skau. 

 11 3

Math scraps/fragments/tablets on assorted subjects: prime number theorem (elementary), zeta functions, automorphic forms, prime number theorem (Chebyshev), Selberg integral, Einsenstein series. 

 11 4

Correspondence (draft) to Jens Erik Fenstad regarding Abel Prize in Norway; interesting comments on a book draft seemingly about Institute for Advanced Study history or Gödel; cute letter from a student admirer (2003); math scraps - enumerating primes, twin primes, etc, plus other topics, e.g. zeta function; SAS envelope with list by Selberg of names of mathematicians involved with prime number-type theorems; excerpt from unknown book pertaining to Einstein; letter about prime number theorem (PNT) from, it appears, Hedi Daboussi (June 1995); 2006 biographical item draft from Indian National Science Academy; some preprints for critique from Jeff Mozzochi. 

 11 5

Schedule for Erwin Schrödinger International Institute for Mathematical Physics (ESI) 1998 meeting in Vienna on zeta function; a review of volume two of Selberg's "Collected Works"; history of Syracuse University's Department of Mathematics (2000) - Selberg features in this history - cover letter by Betty Selberg (2010) - comments on Erdös; several very old pages from what appears to be a lecture on discontinuous groups (perhaps dating to the 1960s); working notes found in desk in study at home for a lecture that appears similar to Uppsala, September 1998, on "Positive Proportion". 

 11 6

More personal things brought in from home by Betty Selberg on March 23, 2010: Los Angeles Times obituary (2007) for Selberg (scanned), clipping from a defunct Norwegian news magazine (1949) - "Dagens navn" article about Atle and prime number theorem (scanned), photograph of three mathematicians including Selberg - Princeton - summer 1948 - color [see FAC SEL 101], big photo of a group of mathematicians including Selberg and possibly Pál Turán - black and white - possibly 1950s [see FAC SEL 102], two clipping-type photos from 1957 Institute for Advanced Study Seminar on Analytic Functions, postcard sent to Selberg and his wife (Hedi) from the 1949 Skandinaviske matematikerkongres with original signatures by a few dozen of the participants. (Processing note from Archives Center staff: the two photographs were moved to the folders of photographs from the Selberg Papers, and can be viewed from the Digital Collections pages: http://cdm.itg.ias.edu/cdm/. They are physically located in Folder 4: Selberg with others, chiefly scholars. The postcard listed was not moved, but can also be viewed from the Digital Collections pages.) 

 11 7

Graphs of Beurling function B(x) from Paul Bateman 1977 

 12 1

Selberg integral - lecture preparations and transparencies; (some pages scanned for website). 

 12 2

Lecture preparations mainly in Norwegian around trace formula and Eisenstein series; see also Box 12, envelope 14. 

 12 3

Lecture preparations around "Linear Operators" paper; lecture preparations on a history lecture, Disquisitiones, etc.; scraps of a lecture preparation "On a conjecture of Kummer"; some lecture preparations around large sieve and density estimates; scanned and available on website: Volume 1 of Collected Works, page 615. 

 12 4

Lecture preparations around trace formula on Hn; transparencies and preparations on distribution of ζ' (1/2 + it) (this is scanned and available on website); transparencies on automorphic forms and admissible weights (scanned a available on website). 

 12 5

Lecture preparations and transparencies on "Hybrid Trace Formula" (available from website); pages of Dennis Hejhal's notes from Selberg's 1984 Bowdoin and Stanford University hybrid trace lectures (13 pp.); 1965 Yeshiva University "Discontinuous Groups" audio transcription and letter from Abe Gelbart (available from website). 

 12 6

Five lecture fragments plus transparencies for equidistribution on discrete subgroups Γ\G (available on website); Tel Aviv lecture abstracts (available on website). 

 12 7

Xerox of Amalfi lecture transparencies (and xerox for scanning); transparencies of an Amalfi-like lecture (post-1989) (and xerox for scanning); transparencies of a still-later Amalfi-like lecture (and xerox for scanning); see also Box 12, Envelope 16. 

 12 8

Uppsala University lecture transparencies (xerox copy created by Dennis Hejhal and scanned). Fall 1997 

 12 9

Seattle lecture on "History of Prime Number Theorem" transparencies plus related materials added by Dennis Hejhal (including part of the lecture preparations) (available on website). 1996 

 12 10

Edited version of Atle Selberg's Hong Kong lectures 1-6 and public lecture (available on website). 

 12 11

Hong Kong lectures (#1-5 plus public lecture) typed from transparencies (available on website). 1998 

 12 12

Lecture 6 from Hong Kong on the topic of Beurling primes including revised transparencies and typed version from original transparencies (available on website). 1998 

 12 13

An envelope with several lecture fragments from previous lectures which was sent January 1992 from Princeton to Atle Selberg in Tel Aviv, which included: survey lecture on Riemann zeta zeros, fragments of an "Amalfi-like" lecture, material on Selberg integral by Greg Anderson (Sept. 1990), two Norwegian lecture fragments related to automorphy factors and weights ("Oslo forelesninger"), five Norwegian lecture fragments headed toward trace formula on Hn, one lecture fragment in English on "Poincaré series, etc." (Hecke relations). 

 12 14

Xerox copy of typescript for "On elementary methods in prime number theory and their limitations"-possibly used in preparing a lecture; lecture fragment in Norwegian similar to 1996 Seattle lecture on prime number theorem. 

 12 15

Scraps of a lecture similar to Amalfi, but with emphasis on "a"-values (available on website); xerox copy of slides from 1999 Mathematical Sciences Research Institute "Positive Proportion" lecture (available on website); xerox copy of 1998 Hong Kong Lecture 7 transparencies on "Positive Proportion" (available on website); xerox copy of typed version of Hong Kong Lecture 7 (available on website). 

 12 16

This seems to be an earlier version of Hong Kong Lecture 7; the claim at end about c/n was not retained in the Hong Kong Lecture; details about justification unclear (available on website); an extra tablet (fragments) touching on Hilbert's inequality and Deane Montgomery's work. 

 12 17

Lecture transparencies and xeroxes on Hx......xH discrete subgroup arithmeticity/rigidity - lecture given at Eidgenössische Technische Hochschule Zürich (ETH) in about 2003 and elsewhere earlier - this work dates back to 1963 (available on website); working fragments on same topic found at home by Betty Selberg; more seroxes of the orginal transparencies made by K. Chandraskharan, who resent the material in June 2004. 

 12 18

Additional lecture fragments on Hx....xH ridigity and arithmeticity (several of these available on website) - rather disorganized - dates to early 1960s through 1970s. 

 12 19

The original transparencies, which were found at Selberg's home, from the Mathematical Sciences Research Institute talk on positive proportion (available on website); Dennis Hejhal notes that he moved these materials from Box 9 to current location. 1999 

 12 20

Preliminary version of 1954 Göttingen Lectures (part 2). Handwritten in blue ink. Page 101 missing. Not identical to final vers. Page 101 also missing on 1950s photostat. 

 13 1

Xerox copy of preliminary version of 1954 Göttingen lecture notes (part 2). Page numbers written in by Selberg. Page 101 again missing. 

 13 2

1950s-era photostatic copy of the preliminary version of the 1954 Göttingen Lectures (part 2). Page 101 also missing here. 

 13 3

2nd xerox copy of prelim version of 1954 Göttingen lecture notes (part 2). Page 101 missing. 

 13 4

Two xerox copies of 1954 Göttingen Lecture Notes (part 2). Made from Göttingen library copy. One by Hejhal 1976. 

 13 5

1954 Göttingen lecture notes (part 2). Proof-correction for Collected Works. June 1987 

 13 6

Transcription of 1954 Göttingen lecture notes, part one. Made by Siegfried Berg. Also Berg's cover letter of 23 Dec 1955. (Reliability of Berg's notes questionable.) 

 13 7

Notes from Selberg's 1954-55 IAS trace formula lectures; Author unknown. Xerox copy. 

 13 8

Copy of Hugh Montgomery's paper from 1987 Oslo Proceedings. Also xerox of a handwritten manuscript of S. Chowla, "On a conjecture of Artin". 

 13 9

Folder from 1988 Nordic Math Congress (Trondheim). 2 pages on sieve theory. 

 13 10

Various fragments in tablets. Largely zeta, SL(2,R)- trace formula, sieves. post-1970. some 1990s 

 13 11

Some copies linked to 1954 Göttingen Lectures in vol. 1 of Collected Works. 

 13 12

From Atle Selberg's desktop: lecture fragments on higher dimensional rigidity/arithmeticity; on page one, Atle Selberg says this is from a series of lectures that followed his survey talk at the 1968 Oslo Congress. 

 13 13A

Two tablets corresponding to part of a lecture series on the trace formula (very similar to Bombay 1956 paper); at least one of the tablets suggests that the lecture was given at the Weizmann institute. 

 13 14A

Part Two of Göttingen lectures; xerox copy that was used for scanning; see Box 13, Envelope 5. 1954 

 13 15A

Part One of Göttingen lectures; xerox copy that was used for scanning. 1954 

 13 16A

From Atle Selberg's desktop: xerox copy of Part Two of Göttingen lectures that was used by Atle Selberg. 1954 

 13 17A

From Atle Selberg's desktop: assorted collection of math fragments, chiefly on trace formula in Hn (some in Norwegian), but also a bit on Beurling/Selberg functions, large sieve, and ζ(s)-a; one page pertaining to Hecke relations and Shimura correspondence, other pages on Z(s). 

 13 18A

A set of "ditto'd" notes, very faded, from a lecture series on Selberg's work - author unknown - date of lectures roughly 9 April 1974 to 15 May 1974 - topics covered include sieves and Selberg trace formula. 

 13 19A

Xerox of preliminary form of 1954 Göttingen lectures; used for scanning; cf. Box 13, Envelope 1. 

 13 20A

Figures for Collected Works, Volume 2; handwritten manuscript for Canadian Journal of Mathematics (1950) paper on primes in arithmetic (scanned); assorted math scraps from Syracuse University days - on primes and sieves. 

 15 1

Manuscript by Richard Bellman related to Eisenstein series; referee request from R. Langer at Duke Mathematical Journal (October 1955). 

 15 2

Original typscript of Über einige arithmetische Identitäten with about fifty-percent of the pages missing (has only pages 1-7). 1936 

 15 3

Nine reprints by Erling Følner sent to Atle Selberg - unknown significance. circa 1954 

 15 4

Correspondence from Ernst Jacobsthal to people at Springer-Verlag concerning W. Blaschke's ongoing anti-Semitism; plus carbon copies from editors at Springer-Verlag. 1950 

 15 5

Xeroxes of picture of Atle Selberg at an unidentified meeting; draft of what appears to be an evalutaion of Wolfgang Schmidt; preprint of Bombieri - On Twin Almost Primes; preprint of Bergman, Models in the Theory of Several Complex Variables (probably early 1950s); copy of Gauthier-Villars Pamphlet (1954) from C. Störmer with reference to Erdös elementary prime number theorem material; preprint of Bombieri remarks on Weil's quadratic functional; folder of a few math notes dated to August 2000 and found by Betty Selberg. 

 15 6

From Atle Selberg's upper right desk drawer: copy of "Demonstration elementaire du theoreme sur la distribution des nombres premiers" from Mathematisch Centrum (Amsterdam, Netherlands); first publication on this; possibly prepared by Johannes Gualtherus van der Corput - no date - only implicit information on page 1 circa 1948 

 15 7

Draft referee reports on two papers of N.C. Ankeny, "The least quadratic non-residue" and "L-series" (by Atle Selberg). 

 15 8

Copy of manuscript "On Diophantine Approximation" (April 1937) by Blichfeldt - by way of Harold Davenport - by way of Harold Bacon - by way of Carl Carlson (Stanford, 1980) - Atle Selberg commented on this; reprint by M.H. Protter on partial differential equations from Transactions of the American Mathematical Society (1951). 

 15 9

From the desk (upper right drawer) of Atle Selberg: 26 December 1953 mathematical letter from C.L. Siegel to Selberg related to automorphic forms and spectral theory - letter influenced Selberg; two printed brochures from the 11th Skandinaviske Mathematikerkongress, Trondheim, August 1949. 

 15 10

From Atle Selberg's desk drawer: J. R. Oppenheimer's letter, November 1998, offering Selberg an Institute permanent membership; J. R. Oppenheimer's letter, January 1951, approving promotion of Selberg to Institute professorship; Oswald Veblen supplementary letter, November 1948; all materials scanned. 

 15 11

From the desk (upper left drawer) of Atle Selberg: original typescriipt for The Journal of the Indian Mathematical Society paper on Trace Formula, carbon copy, missing page 50 (last page) (scanned). 1956 

 15 12

Seventy-fifth birthday congratulatory letters from: Henrik Selberg, Universitetet i Oslo, Universitetet i Tromsø, Norwegian Research Minister, Universitetet i Bergen, and the Norwegian University of Science and Technology-Trondheim (first signer: Nils Baas). 1992 

 15 13

Institute for Advanced Study administrative business in which Selberg was involved, including: report on Jean Leray; report on Jean-Pierre Serre; Conference on Analytic Functions, September 2-13, 1957; January 1973-October 1, 1975, folder possibly related to Robert Bellah; October 1972-1974 folder regarding Board of Trustees candidates (J.L. Doob/G.D. Mostow); folder from 1963 referencing Lars Hörmander and Harish-Chandra appointments with a letter by Oppenheimer. 

 15 S1

Report and material about André Weil regarding his appointment to the Institute for Advanced Study. 1957 

 15 S2

From Selberg's desk, letters from (unless otherwise noted) the following: to Q.I. Rahman, Urbana, Annals of Mathematics, December 1958; fax from Erik Hjorth-Hansen, March 2001; F. Mautner, Johns Hopkins, March 1953; Norske Videnskaps-Akademie, December 2001; Chandler Davis, Math Intelligencer, March 1991; George Greaves, November 1993; draft letter to Ram Murty, Canada, April 1991; two letters (January 1993, October 1997) - M.C. Liu, Hong Kong; Chandrasekharan, January 1990; reprint request from H. Kloosterman, July 1950; Boas, Math Reviews, October 1949; piece of a letter from John Nash about pseudo-primes, probably 1950s; two letters - K.Y. Chan, Hong Kong - to him, January 1998, and from him, February 1998; two letters (November 1996 and January 1997) - Pan Chengbiao, Beijing; Joachim Heinze, Spring-Verlag, July 1987; K. Chandrasekharan, October 2005; Paul Bateman , Urbana, about Prime Number Theorem history and Erdös, June 1977; Hel Braun to Hedi Selberg about Carl L. Siegel's death, 18 April 1981; two letters (both 1972: 19 August and 20 September) - Hans Maass; Viggo Brun - experts' report on professorship in Oslo - Atle Selberg was first and Henrik Selberg was second in rankings - 24 May 1949; Hermann Weyl and one xerox copy, 19 September 1952; copy of reply to Hermann Weyl, October 1952. 

 15 S3
Box

English translation (by Imre Toth) of letter from Hel Braun to Hedi Selberg about Carl L. Siegel's death, 18 April 1981. 

 1

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Photographs 1920-2007   0.5 linear feet 1 box

Scope and Contents note

The Photographs series consists primarily of prints featuring Atle Selberg, members of his family, friends, and colleagues.

Existence and Location of Copies note

The entirety of the Photographs series has been digitized and is available online.

Atle Selberg photographs, 1920-2007

[http://cdm.itg.ias.edu/cdm/search/collection/coll3/searchterm/Atle Selberg papers]

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