This list of publications (included for the reader's convenience) is taken from volume 2 of Selberg's Collected Papers. Note the addition of 3 subsidiary works (in Norwegian) that were omitted there; cf. items 46-48.

The October 2008 issue of the Bulletin of the American Mathematical Society featured a number of articles pertaining to Atle Selberg and his work. The excerpt given below served as its introduction.

This wide-ranging, retrospective interview with Selberg was done in June 1989 at IAS; the interviewer was Betsy Devine. It is currently unpublished, and is part of the "Oral History Project" at IAS.

The copy found in Selberg's office was printed in 1990. On the basis of this and the short note that Betsy Devine attached to part 2, it seems likely that this version was proofread by Selberg.

Subsequent to Betsy Devine's interview, Selberg was interviewed several other times. The file attached below comes from the February 12, 1991 issue of the "Princeton Packet", a weekly newspaper in Princeton.

The wide-ranging interview done by N. Baas and C. Skau in November 2005 can be found here (in both English and Norwegian).

A third interview, conducted in June 1999, can be found in the book, Fascinating Mathematical People: Interviews and Memoirs, ed. by D. Albers and G. Alexanderson, Princeton University Press, 2011, pp.254--273.

Here are two clippings and a postcard from August 1949.

The first clipping is from the Trondheim newspaper, Nidaros. It captures some of the atmosphere at Selberg's lecture on the elementary proof of the prime number theorem (on 8/22/49) at the Scandinavian Math Congress.

The second clipping is from a now defunct, rotogravure-type, Norwegian magazine called Aktuell. It highlights Atle Selberg as "today's name" in connection with Selberg's work with the primes. (An astute reader would notice that there was an error in the text, viz., the assertion that Selberg went to school in Langesund. He didn't. In particular, there is no mention of Gjovik, where Selberg went to high school and his father was the school's rektor. The handwriting in the left margin of copy #2 would appear to be that of a family member (his mother?), who noted the error and went on to say that "pappa would not be happy, those in Gjovik would notice".)

Since Selberg apparently needed to depart early from the Trondheim Congress, the group postcard that Ernst Jacobsthal organized was clearly a nice momento.

These clippings and a number of others from the same time period were found under a pile of papers on a shelf near Selberg's desk. Likewise for the postcard.

The files below appear to be three drafts of a lecture on elementary methods and generalized (Beurling) primes that Selberg gave during the 1948-49 academic year when he was at Syracuse University. The first two go together in terms of their initial hypotheses.

Lecture 6 in the 1998 Hong Kong lecture series focuses on much the same material. The underlying technique is of course very closely tied to that of item #22 in the list of publications.

Based on the type of paper and black ink used, this draft manuscript on the remainder term in the circle problem appears to date from the late 1940s or early 50s. The penultimate page, written in blue ink on a sheet of notebook paper, seems to be a supplemental sheet -- possibly consulted during a lecture. The final page is a fragment that appears to go with the pages in black ink.

The manuscript was found on a shelf close to Selberg's desk, except for page 10 and the fragment, which turned up in one of the desk drawers.

The attached file is a fragment of what appears to be a lecture from the late 1940s on violations of Gram's law. (The pages are written in Selberg's characteristic light blue ink from that period and are of standard American size. They were found on a shelf near his office desk.)

The material is closely connected with the assertions made in section IV of Selberg's 1946 Scandinavian Math Congress paper, "The zeta-function and the Riemann hypothesis"; cf. item #17 the list of publications.

Scan of a xerox copy of the original manuscript found in the Math Institute Library at the University of Gottingen. This work corresponds to item #39 in the Collected Papers and the list of publications.

Some differences here-and-there compared to the final (Gottingen Math Library) version, particularly in section 10. Page 101 seems to be lost, unfortunately. Compare section 4 in Selberg's 1956 J. Indian Math. Society paper.

This transcription of "Part 1" by Siegfried Berg was uncovered on a dusty shelf in Selberg's office. Its reliability is questionable. It is included here chiefly to give readers a fuller picture of the overall content of Selberg's 1954 lecture series.

The identity of the note-taker is unknown. The current best guess is either Josephine Mitchell or Lowell Schoenfeld, based partly on IAS membership records and a conversation with Paul Malliavin, who attended the lectures. The copy of the notes found in Selberg's office was given to him many years ago by Burt Randol. (Randol, in turn, recalls receiving his copy from Harry Rauch, whose stay at IAS took place during the two-year period 1949-51.)

In 1962, Selberg lectured at an inaugural science conference at Yeshiva University. His topic was "Recent developments and open problems in the theory of discontinuous groups." The second file below is a partially corrected audio transcript from that talk. It was found on a shelf near Selberg's desk. (The tape was presumably kept by Yeshiva.) File #1 gives background; it would seem from Gelbart's letter that someone other than Selberg made the bulk of the handwritten corrections.

From a set of transparencies found on a shelf near Selberg's desk. The results stated herein are old ones, dating back to at least the 1960s; the one-dimensional case was mentioned to several people already around 1973.

There is some overlap here with item #28 in the list of publications.

On the last page of Selberg's 1972 paper "Remarks on sieves' (item #37 in the list of publications), reference is made to a large sieve inequality for pseudocharacters and its application to density-type estimates for zeros of Dirichlet L-series.

The first file below, dating from around 1970, appears to be a set of Selberg's working notes from a lecture on this topic. File 2 shows some additional pages from the same manila folder found on the shelves next to Selberg's desk. The third file is a scan of the relevant pages from item 37.

A number of unpublished fragments concerning "density theorems" for the zeros of the Riemann zeta-function turned up in Selberg's office. Some were in the cupboards, others on the big tabletop.

The six files below are some reasonably coherent portions of this material. They appear to date from the late 1960s (based on internal references) and to be lecture preparations of one type or another. Based on a marginal note, part of the technique utilized in file #6 appears to date back to 1945-46.

In the mid-1970s, Selberg gave a lecture at one of Rockefeller University's "Number Theory Days" under the general heading of spectral theory and equidistribution properties of discrete groups. The same material was included in a lecture at Stanford in 1980. Following his passing in 2007, several (European A4-size) lecture transparencies on this theme plus a number of loosely organized, much older-looking, cognate working papers were found in Selberg's office. The files below are scans of this material.

File 1 shows the transparencies: these may well have formed part of one of Selberg's 1991 Tel Aviv lectures (cf. the corresponding 'bullet' one level up, under Tel Aviv abstracts). Files 2 through 4 (scanned from American-sized pages) appear to be from the 1970s; file 5 (from a bit newer, A4-size) is less clear.

The last page of file 2 was found mixed in among papers on a completely different topic. It is now presumably back in the right place.

During the 1980s and 90s, Selberg occasionally lectured on what he called "the hybrid trace formula". a special kind of trace formula associated with Hilbert modular-type groups. In 1984, for instance, he lectured on this topic at both Stanford and the AMS-MAA-SIAM Joint Summer Conference on Trace Formulas held at Bowdoin College. Aside from the final entry below, the attached scans are basically copies of his transparencies together with some fragments of his working notes from these 2 lectures.

Additional places where he lectured on this matter include Stillwater(1984), Tata Institute (January 1988), and Institut Mittag-Leffler (1995). His talk at the Tata Institute was given during the Ramanujan Centenary; file 4 appears to be its abstract. The results themselves date back to the early 1970s or before.

This set of transparencies concerning derivatives of zeta-functions was found on a shelf near Selberg's desk. The approach developed herein was mentioned to D. Hejhal during a conversation at the 1988 Nordic Math Congress in Trondheim. Where Selberg actually lectured on this topic is currently unclear. (A look at page 1 shows that the date for such a lecture would have to be September 1989 or later.)

This collection of files centers on Selberg's September 1989 Amalfi lecture. The first file is a scan of the original transparencies; the legal-paper-size tablet that Selberg used in first writing out this lecture can be found in the archive at IAS.

Files 2 and 3 are scans of some transparencies very similar to the Amalfi lecture; where they were used is not clear. Note that file 3 differs slightly from file 2 on pages 5, 6*, and 10.

File 4 is a scan of some fragments in a folder (most likely used in a lecture) focusing chiefly on the "a"-value part of the Amalfi lecture. No transparencies were found for this.

File 5 is a scan of another fragment from an Amalfi-like lecture (or lecture series); the pages fill in several details from the original talk.

Particularly after 1979 or so, Selberg occasionally lectured on material related to his celebrated 1944 multiple integral; cf. item #14 in the list of publications. Among the places he spoke were LaJolla (1980), Berkeley (1980), and Tel Aviv (1991).

The first two scans are sets of transparencies from lectures that he gave in the early 1990s. The 3rd scan appears to be a supplement to the 2nd lecture. The 4th consists of some fragments of his working notes that he kept in a folder together with the transparencies. The fragments in file 5 were found in a different location. Note especially the last 6 lines on page 1, which make reference to item #7 (sections 2 and 3) and work by E. Bombieri on prime numbers.

Selberg gave a series of three lectures at Tel Aviv University in November 1991. The third lecture included a sketch of a very curious spectral-theoretic proof of the classical prime number theorem. Additional details concerning the results outlined in that lecture can be found under the 'equidistribution and spectral theory' subject heading above.

In 1995, Selberg lectured on arithmeticity at ETH in Zurich. The original transparencies for this talk, along with a xerox copy of some transparencies used in a very similar one, turned up at home in a folder labelled "1963".

When Selberg had need of these transparencies in 2003, he was unable to locate them. He asked Chandrasekharan at ETH to make a copy of the xerox copy that Selberg had sent him back in 1995. Files 1 and 2 below correspond to the ETH talk; file 3 to the related one. The work described in these lectures dates back to the early 1960s and early 70s; it has a very close link to item #35 in the list of publications.

The last 7 files, S1--S7 [added June 2013], are some additional lecture fragments and preparations taken from the relevant folders. The first four of these make reference to the L-function connection cited in section 7.5 of item #35.

Here is a scan of the transparencies from Selberg's lecture at the 1996 Seattle meeting, "In Celebration of the Centenary of the Proof of the Prime Number Theorem", sponsored by the American Institute of Mathematics.

This is a copy of the transparencies that Selberg used in his September 1997 talk at Uppsala University. The full title was: "On the value distribution of Dirichlet series with Euler product and functional equation and of finite linear combinations of such functions."

Selberg lectured in Hong Kong during May 1998. Attached are copies of his transparencies, courtesy of Kai-man Tsang. The files ending in "T" are scans of some typed transcriptions found in Selberg's office.

Lecture 6 was on Beurling's generalized primes. A snag apparently occurred during the lecture; see page 14 (starting 4th line from the bottom) in lec6 and page 46 (line 8) in lec6T. The revised transparencies found in Selberg's office are attached here as "lec6R". Selberg first lectured on this topic around 1948-49 when he was at Syracuse University.

Lecture 0 was a public lecture on the history of the prime number theorem, essentially identical to the one given in Seattle in 1996.

Here is a version of the Hong Kong lecture series edited and annotated by Yuan Wang. (Courtesy of Kai-man Tsang.)

Selberg's celebrated positive proportion result concerning zeros of linear combinations of L-functions was first obtained early in 1998 at age 80, following some preliminary work that he did during his stay in Uppsala the preceding Fall.

The first two files below are scans of the transparencies from two of his lectures on this topic: Hong Kong (May 1998) and MSRI (June 1999). The latter had the title "Linear combinations of L-functions and zeros on the critical line". The former was a supplement to his prime number theory lectures there. (File 3 is simply the typed version of the Hong Kong talk.)

This topic is very closely connected with items #9 and 44 in Selberg's list of publications. See also items 10 and 17 (p. 196).

In response to several questions raised since files 1--3 were uploaded in June 2012, five additional variants have now been appended. The most important of these is file #4, a scan of a revised version of the 1999 MSRI lecture that was found at home in Selberg's study. The file contains some additional assertions, as well as brief indications about possible improvements in the 1999 version. (Those in the audience at MSRI may remember Selberg's impromptu remarks there about several of these matters. File 4 should probably be viewed as a bit tentative, since no further details concerning the revisions could be located among Selberg's papers, either in his office or at home.)

One of the improvements that Selberg mentions pertains to obtaining (c/n)TlogT when Lambda = 1/2. Files 6 and 8 (below) also cite this result, albeit briefly.

Files 5--7 are scans of some pages found on the windowsill near Selberg's desk. File 5 is quite similar to the MSRI talk and is likely part of the preparation for that lecture. The pages scanned in file 6 have a certain resemblance to both the MSRI lecture and its revision; unfortunately, they stop at page 12. The natural conjecture is that they are part of the preparations for a lecture subsequent to MSRI. File 7 is a scan of a xerox copy of the transparencies that Selberg used in his 1998 talk at Uppsala; it is interesting to compare file 7 with file 5.

The close similarity of file 8 to Selberg's Hong Kong lecture (i.e., file 1) suggests that the former may be an earlier draft of what he ultimately decided to present there. (The discrepancy with file 1, page 15, fits with a comment that Selberg made to D.H. in July 1998 that the case alpha = 1 encountered a technical snag, and that his current-best estimate had coefficient c/(n log n).) The transparencies scanned in file 8 were found on a shelf near Selberg's desk.