Atle Selberg

Atle Selberg

Atle Selberg (June 14, 1917 – August 6, 2007) was a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory.

Early years

Selberg was born in Langesund, Norway. 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.

During the war he fought against the German invasion of Norway, and was imprisoned a few times. He studied at the University of Oslo and completed his Ph.D. 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 proof of the prime number theorem. Paul Erdős used Selberg's work to obtain 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.

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 eigenvalues of the Laplacian, which is analogous to the duality between the prime numbers 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 playwright Mustapha Matura.

He died at home on 6 August 2007, of heart failure. [cite news |first= |last= |authorlink= |coauthors= |title=Atle Selberg, 90, Lauded Mathematician, Dies |publisher=New York Times |date=2007-08-17 |accessdate=2007-07-21 ]

elected publications

*"Atle Selberg Collected Papers: 1" (Springer-Verlag, Heidelberg), ISBN 0387183892
*"Collected Papers" (Springer-Verlag, Heidelberg Mai 1998), ISBN 3540506268

ee also

*Critical line theorem
*Chowla-Selberg formula
*Selberg class
*Selberg integral
*Selberg trace formula
*Selberg zeta function



first=Nils A.|last= Baas|first2= Christian F.|last2= Skau
journal= Bull. Amer. Math. Soc. |volume=45 |year=2008|pages= 617-649
title=The lord of the numbers, Atle Selberg. On his life and mathematics
Interview with Selberg

*citation|last=Selberg |url= |title=Reflections Around the Ramanujan Centenary|year=1996
* [ Obituary at IAS]
* [ Obituary in "The Times"]

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  • Atle Selberg — (* 14. Juni 1917 in Langesund, Norwegen; † 6. August 2007 in Princeton, New Jersey) war ein norwegisch US amerikanischer Mathematiker, der 1950 mit der Fields Medaille für seine herausragenden Arbeiten auf dem Gebiet der Zah …   Deutsch Wikipedia

  • Atle Selberg — (né le 17 juin 1917 à Langesund (en) (Norvège) et mort le 6 août 2007 à Princeton (New Jersey)) est un mathématicien …   Wikipédia en Français

  • Atle Selberg — Saltar a navegación, búsqueda Atle Selberg Atle Selberg (14 de junio de 1917 6 de agosto de 2007) fue un matemático noruego, conocido por sus trabajos en la teoría analítica de los números y sobre la hipótesis d …   Wikipedia Español

  • Selberg — steht für: Atle Selberg (1917–2007), norwegisch US amerikanischer Mathematiker Selberg (Donnersbergkreis), ein Berg im Donnersbergkreis Selberg (Landkreis Kusel), ein Berg im Landkreis Kusel Kleiner Selberg, ein Berg in Vlotho im Landkreis… …   Deutsch Wikipedia

  • Selberg — can refer to:* Atle Selberg, a Norwegian mathematician * Erik Selberg, an American computer scientist …   Wikipedia

  • Selberg integral — In mathematics the Selberg integral is a generalization of Euler beta function to n dimensions introduced and proven by Atle Selberg (1944). Contents 1 Selberg s integral formula 2 Aomoto s integral formula 3 Mehta s integral …   Wikipedia

  • Selberg class — In mathematics, the Selberg class S is an axiomatic definition of the class of L functions. The members of the class are Dirichlet series which obey four axioms that seem to capture the essential properties satisfied by most functions that are… …   Wikipedia

  • Selberg trace formula — In mathematics, the Selberg trace formula is a central result, or area of research, in non commutative harmonic analysis. It provides an expression for the trace, in a sense suitably generalising that of the trace of a matrix, for suitable… …   Wikipedia

  • Selberg zeta function — The Selberg zeta function was introduced by Atle Selberg in the 1950s. It is analogous to the famous Riemann zeta function :zeta(s) = prod {pinmathbb{P frac{1}{1 p^{ s where mathbb{P} is the set of prime numbers. The Selberg zeta function uses… …   Wikipedia

  • Selberg sieve — In mathematics, in the field of number theory, the Selberg sieve is a technique for estimating the size of sifted sets of positive integers which satisfy a set of conditions which are expressed by congruences. It was developed by Atle Selberg in… …   Wikipedia

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