Atle Selberg

Atle Selberg (* 14. June 1917 in Langesund , Norway ; † 6. August 2007 in Princeton , New Jersey ) was a Norwegian-American mathematician who in 1950 with the Fields Medal for his outstanding work in the field of number theory awarded has been.

Life

Selberg's interest in mathematics began as a schoolboy. In his youth he enthusiastically read the collected publications of S. Ramanujan and began his own mathematical research. The next influence came from Erich Hecke , from whom he heard a lecture at the International Mathematical Conference in Oslo in 1936 .

He studied mathematics at the University of Oslo until his doctorate in 1943 and stayed there until 1947. In the same year he married Hedvig Liebermann and went to the United States . From 1947 to 1948 he worked at the Institute for Advanced Study in Princeton and then moved for a short time to the University of Syracuse . In 1949 he returned to the Institute for Advanced Study as a permanent member and at the same time was appointed Professor of Mathematics at Princeton in 1951. In 1987 Selberg retired from Princeton, but without completely stopping his scientific work. After the death of his wife Hedvig in 1995, he married the American Betty Compton for the second time. According to his family, Atle Selberg died of heart failure at his Princeton home on August 6, 2007, at the age of 90. In addition to his wife Betty, he left behind a son Lars and a daughter Ingrid from his first marriage and two stepdaughters from his second marriage. His daughter Ingrid Selberg is a writer, married to the Trinidadian playwright Mustapha Matura .

Act

Selberg was first known for his "elementary" (that is, without using function theory) proof of the prime number theorem in 1948, roughly at the same time as Paul Erdős . The question of the interference in the evidence that arose while both were at Princeton has long been a matter of dispute. Even in the relative isolation of the war years in Norway, he also proved that at least a small percentage of the non-trivial zeros of the Riemann zeta function lie on the critical line (with real part 1/2) (from Norman Levinson 1974 to 1/3 and from Brian Conrey improved to 2/5 in 1989). That was an important step in the field of the Riemann Conjecture , which is still open today . Before that, Hardy and Littlewood had only been able to show that an infinite number of zeros lie on the critical straight line. In 1947 he improved the sieving method of the Norwegian mathematician Viggo Brun in analytical number theory (Selberg sieve). The trace formula of Selberg (1956) presented similar to explicit formulas of the analytical theory of numbers a connection between sums over the eigenvalues (the track ) of the Laplace-Beltrami operator on compact Riemann surfaces and sums over the geometric range, the lengths of the closed geodesic curves , (the latter take on the role of the prime numbers in the corresponding formulas from analytic number theory, while the zeros of the zeta function correspond to the eigenvalues of the Laplace operator). In this context he also introduced an analogue to the Riemann zeta function, the Selberg zeta function (with prime numbers replaced by the lengths of the closed geodetic orbits). He also worked on automorphic functions and modular forms (trace formula by Martin Eichler and Selberg, here the trace of the Hecke operators , operating in the space of modular forms).

Awards

In 1950 Selberg was awarded the Fields Medal at the International Congress of Mathematicians in Harvard (Lecture: The general sieve method and its place in prime number theory). In 1962 he gave a plenary lecture at the International Congress of Mathematicians in Stockholm (Discontinuous Groups and Harmonic Analysis). Other honors for his work were his membership in the Norwegian Academy of Sciences , the Royal Danish Academy of Sciences , the American Academy of Arts and Sciences (1960) and the Indian National Science Academy (Indian Academy of Sciences), as well as an honorary membership of London Mathematical Society . In 1972 Selberg received an honorary doctorate from the University of Trondheim , and in 1986, together with Samuel Eilenberg, the internationally renowned Wolf Prize in Mathematics.

Fonts

Collected papers. Volume 1: Springer, Heidelberg 1989, ISBN 3-540-18389-2 ; Volume 2: Springer, Heidelberg 1991, ISBN 3-540-50626-8 .

literature

Egil Aubert (Ed.): Number Theory, Trace Formulas, and Discrete Groups. Symposium in Honor of Atle Selberg, Oslo, Norway, July 1987. Academic Press, Boston 1989, ISBN 0-12-067570-6 .
Atle Selberg. In: Encyclopædia Britannica.
Peter Sarnak , Dennis Hejhal : Some comments on Selbergs Mathematics. In: BAMS. 2008.
Skau Baas: The Lord of the Numbers. Atle Selberg, On his life and mathematics. In: BAMS. 2008.
Hejhal (Ed.): Remembering Atle Selberg. Notices, AMS 2009.
Donald J. Albers, Gerald L. Alexanderson Fascinating Mathematical People: Interviews and Memoirs , Princeton University Press 2011

Web links

Literature by and about Atle Selberg in the catalog of the German National Library
John J. O'Connor, Edmund F. Robertson : Atle Selberg. In: MacTutor History of Mathematics archive .
Website on IAS with publications (English)
Atle Selberg, 90, Lauded Mathematician, Dies. In: NY Times. 17th August 2007.

Individual evidence

↑ For Paul Erdős, too, an inequality by Selberg was the starting point. In Joel Spencer, Ronald Graham: The Elementary Proof of the Prime Number Theorem. In: Mathematical Intelligencer. No. 3, 2009, memories from Straus are reproduced.

personal data
SURNAME	Selberg, Atle
BRIEF DESCRIPTION	Norwegian mathematician and university professor
DATE OF BIRTH	June 14, 1917
PLACE OF BIRTH	Langesund
DATE OF DEATH	August 6, 2007
Place of death	Princeton

[1] For Paul Erdős, too, an inequality by Selberg was the starting point. In Joel Spencer, Ronald Graham: The Elementary Proof of the Prime Number Theorem. In: Mathematical Intelligencer. No. 3, 2009, memories from Straus are reproduced.