'''Atle Selberg''' ([[June 14]], [[1917]] - [[August 6]], [[2007]]) was a [[Norway|Norwegian]] [[mathematician]] known for his work in [[analytic number theory]], and in the theory of [[automorphic form]]s, in particular bringing them into relation with [[spectral theory]].

== Early years ==
Selberg was born in [[Langesund]], [[Norway]].
<!-- There seems to be no source for the following anecdote, and the reference given does not mention Selberg:
His first result came at age 14 when he rediscovered [[Johann Bernoulli]]'s remarkable 1697 formula
:<math>\sum_{n=1}^\infty n^{-n} = \int_0^1 x^{-x} dx\quad\quad(=1.291285997...)</math>
which he published as a problem in the book ''Problems and Theorems in Analysis'' (part I, problem 160) by [[Pólya]] and [[Gábor Szegö]].
-->
While he was still at school he was influenced by the work of [[Srinivasa Ramanujan]] and
he discovered the exact analytical formula for the partition function as suggested by the works of
Ramanujan, however, this result was first published by Hans Rademacher. Selberg makes some very interesting
observations about himself and Ramanujan in his
[http://www.ias.ac.in/resonance/Dec1996/pdf/Dec1996Reflections.pdf ''Reflections Around the Ramanujan Centenary''].
He studied at the [[University of Oslo]] and completed his dr. philos. ([[Ph.D.]]) grade in [[1943]].

== Second world war ==
During the [[second world war]] he worked in isolation due to the German military occupation of [[Norway]]. After the war his accomplishments became known, including a proof that a positive proportion of the zeros of the [[Riemann zeta function]] lie on the line Re(s)=1/2. After the war he turned to [[sieve theory]], a previously neglected topic which Selberg's work brought into prominence. In a [[1947]] paper he introduced the [[Selberg sieve]], a method well adapted in particular to providing auxiliary upper bounds, and which contributed to [[Chen's theorem]], among other important results. Then in [[1948]] Selberg gave an elementary [[mathematical proof|proof]] of the [[prime number theorem]]. [[Paul Erdős]], using a crucial result of Selberg, also obtained a proof around the same time, leading to a dispute between them about to whom this result should primarily be attributed. For all these accomplishments Selberg received the [[1950]] [[Fields Medal]]. He was the oldest living Fields Medalist at the time of his death.

== Institute for Advanced Study ==
Selberg moved to the [[United States]] and settled at the [[Institute for Advanced Study]] in [[Princeton, New Jersey]] in the [[1950s]] where he remained until his death. During the 1950s he worked on introducing [[spectral theory]] into [[number theory]], culminating in his development of the [[Selberg trace formula]], the most famous and influential of his results. This establishes a duality between the length spectrum of a [[compact Riemann surface]] and the [[eigenvalue]]s of the [[Laplacian]], which is analogous to the duality between the [[prime number]]s and the zeros of the zeta function. He was awarded the [[1986]] [[Wolf Prize in Mathematics]].

Selberg received many distinctions for his work in addition to the [[Fields Medal]] and [[Wolf Prize]]. He was elected to the Norwegian Academy of Sciences, the Royal Danish Academy of Sciences and the [[American Academy of Arts and Sciences]].

Selberg had two children, Ingrid Selberg and Lars Selberg. Ingrid Selberg is married to well known playwright [[Mustapha Matura]].

==Death==
He died at home on [[6 August]] [[2007]], of heart failure. <ref>{{cite news |first= |last= |authorlink= |coauthors= |title=Atle Selberg, 90, Lauded Mathematician, Dies |url= |quote=Atle Selberg, a mathematician whose theoretical work on the properties of numbers was recognized with the [[Fields Medal]] and other major prizes, died Aug. 6 at his home in [[Princeton, New Jersey]] He was 90. The cause was heart failure, his family said. As a young mathematician, Dr. Selberg was first widely recognized for a major contribution to the study of [[prime numbers]], which are evenly divisible only by 1 and themselves. |publisher=[[New York Times]] |date=August 17, 2007 |accessdate=2007-07-21 }}</ref>

==Selected publications==
*''Collected Papers I.'' (Springer-Verlag, Heidelberg, 1989), ISBN 3540183892
*''Atle Selberg Collected Papers: 001'' (Springer-Verlag, Heidelberg), ISBN 0387183892
*''Collected Papers'' (Springer-Verlag, Heidelberg Mai 1998), ISBN 3540506268

==See also==

*[[Critical line theorem]]
*[[Chowla-Selberg formula]]
*[[Selberg zeta function]]
*[[Selberg trace formula]]

==References==
{{reflist}}

==Further reading==
*A. Selberg, ''Collected works'', vol I ISBN 0-387-18389-2
* {{MacTutor Biography|id=Selberg}}
* {{Britannica|9089363}}
* [http://www.ias.edu/newsroom/announcements/view/1186683853.html Obituary at IAS]
* [http://www.timesonline.co.uk/tol/comment/obituaries/article2477242.ece Obituary in ''The Times'']
{{Fields medalists}}
{{Wolf Prize in Mathematics}}

{{DEFAULTSORT:Selberg, Atle}}

[[Category:Norwegian mathematicians]]
[[Category:20th century mathematicians]]
[[Category:Fields Medalists]]
[[Category:Institute for Advanced Study faculty]]
[[Category:Number theorists]]
[[Category:Wolf Prize in Mathematics laureates]]
[[Category:University of Oslo alumni]]
[[Category:1917 births]]
[[Category:2007 deaths]]

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