Atle Selberg

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Atle Selberg (14 June 1917 – 6 August 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. He was awarded the Fields Medal in 1950.


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 several times. He studied at the University of Oslo and completed his Ph.D. in 1943.

Second world war

During World War II he worked in isolation due to the German 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)=\frac{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.[1] 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. In its simplest form, this establishes a duality between the lengths of closed geodesics on 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.

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