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Atle Selberg

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Wikipedia

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. Selberg makes some observations about himself and Ramanujan in his Reflections Around the Ramanujan Centenary

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 also obtained a proof around the same time, leading to a dispute between them about to whom this result should primarily be attributed. Selberg and Erdos had agreed to publish their work in back-to-back papers in the same journal, explaining the work each had done and sharing the credit. But at the last minute Selberg (who, it was said, had overheard himself being slighted by colleagues) raced ahead with his proof and published first. 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 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.

Death

He died at home on 6 August 2007, of heart failure.

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

References