Person: Selberg, Atle
Atle Selberg was a Norwegian mathematician known for his work in analytic number theory and on discrete groups and automorphic forms.
Mathematical Profile (Excerpt):
- Ole Selberg was a school teacher of mathematics who, at age 48, was awarded his doctorate from the University of Oslo for his thesis Ein Beitrag zur Theorie der algebraisch auflösbaren Gleichungen von Primzahlgrad Ⓣ(A contribution to the theory of resolvable algebraic equations of prime degree).
- Henrik Selberg (1906-1993) was born in Bergen.
- The twins Sigmund Selberg (1910-1994) and Arne Selberg (1910-1994) were born on 11 August 1910 in Langesund.
- However, Stormer's lecture notes began by introducing the real numbers with Dedekind cuts which baffled Selberg.
- Selberg was about 17 years old when he came across Ramanujan's collected works which Sigmund had taken out of the university library and brought home.
- Stormer had published an article about Ramanujan in the Norsk Matematisk Tidsskrift, and Selberg had read this too.
- Inspired by reading about Ramanujan and reading his work, Selberg turned to study number theory and began to make his own mathematical explorations.
- It is, therefore, fair to say that Selberg became a number theorist while still at high school.
- Mathematics wasn't the only topic that Selberg studied on his own while at high school for he also taught himself foreign languages.
- In 1935 Selberg graduated from the high school in Gjovik and matriculated at the University of Oslo.
- Another major influence on Selberg's mathematical development was a lecture by Erich Hecke at the International Mathematical Conference in Oslo in 1936.
- Selberg spent most of his time in Uppsala working in the library, then returned to Oslo in December 1939.
- Immediately after the examination, Selberg was arrested by the Germans and put in prison but was released on condition that he left Oslo and returned to Gjovik where his parents were living.
- Shortly after marrying, the Selbergs went to the United States where Atle spent the academic year 1947-48 at the Institute for Advanced Study in Princeton.
- Paul Erdős had arrived at the Institute while Selberg was in Canada and they met as soon as he returned.
- It was at this time that Selberg and Erdős arrived at an elementary proof of the prime number theorem.
- In 1951 Selberg was promoted to professor at Princeton.
- In 1950 Selberg was awarded a Fields Medal at the International Congress of Mathematicians at Harvard.
- In 1949 Selberg and Erdős found an elementary proof that makes no use of complex function theory.
- Subsequent events are not entirely clear but Selberg published two papers An elementary proof of the prime number theorem and An elementary proof of Dirichlet's theorem about primes in an arithmetic progression in volume 50 of the Annals of Mathematics.
- It is not too difficult to see where the misunderstanding between Selberg and Erdős arose.
- Selberg and Erdős are at the opposite extremes - most of Erdős's work is published in joint papers while Selberg has hardly any joint publications.
- Selberg used his trace formula to prove that the "Selberg zeta function" of a Riemann surface satisfies an analogue of the Riemann hypothesis.
- the Rankin-Selberg method, the "mollifier" device in the theory of Riemann's zeta function with its deep applications to zeros on or near the critical line and with Selberg's sieve as a by-product, ...
- Selberg's trace formula, Selberg's zeta function, ...
- Selberg's collected papers were published in two volumes (1989, 1991).
- And thirdly, a lot of highly interesting mathematics comes into daylight via the two volumes of Selberg's collected papers ...
- Selberg was one of the four editors of Axel Thue's Selected mathematical papers published in Oslo in 1977.
- In 1989 Selberg published Reflections around the Ramanujan centenary which is the text of a talk he gave at the conclusion of the Ramanujan Centenary Conference in January 1988 at the Tata Institute in Bombay.
- This tribute to Ramanujan, on the 100th aniversary of his birth, shows the important influence that Ramanujan had in Selberg's mathematical development.
- Selberg has received many distinctions for his work in addition to the Fields Medal.
- In early work, Professor Atle Selberg proved that the zeros of the Riemann zeta function on the critical line have positive density.
- His ideas on sieves led him to his celebrated 'Selberg formula' which is the basis of his elementary proof of the prime number theorem.
- Atle was one such mathematician; he was a mathematician's mathematician.
Born 14 June 1917, Langesund, Norway. Died 6 August 2007, Princeton, New Jersey, USA.
View full biography at MacTutor
Tags relevant for this person:
Prize Fields Medal, Origin Norway, Prize Wolf
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References
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive
