Hugh Montgomery (mathematician)

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Montgomery in Oberwolfach 2008

Hugh Lowell Montgomery (born August 26, 1944 in Muncie , Indiana ) is an American mathematician who deals with analytical number theory and harmonic analysis .

Live and act

Montgomery received his PhD from Cambridge University in 1972 with Harold Davenport . In 1973 he also received the Cambridge University Adams Prize. In 1970/71 and 1976/77 he was at the Institute for Advanced Study . He is a professor at the University of Michigan at Ann Arbor .

With Norman Levinson he showed in 1973 that a third of the zeros of the Riemann zeta function lie on the critical straight line.

Montgomery discovered pair correlations of the zeros of the Riemann zeta function , which, as emerged from discussions with the mathematical physicist Freeman Dyson at the Institute for Advanced Study in the early 1970s, have connections to the distribution of the eigenvalues ​​of random matrices. This gave rise to a new approach to studying the Riemann zeta function and other zeta functions in mathematics. He also studied the Great Sieve method.

He wrote a standard book on elementary number theory and a textbook on analytic number theory with Ivan Niven and Herbert Zuckerman.

In 1974 he received the Salem Prize and in 1975 the Henry Russell Award. In 1974 he was invited speaker at the International Congress of Mathematicians in Vancouver (Distribution of zeros of the Riemann Zeta Function). He is a fellow of the American Mathematical Society . In 1974 he became a Sloan Research Fellow .

Brian Conrey is one of his PhD students .

Fonts

  • Topics in multiplicative number theory , Springer, Lecture Notes in Mathematics 227, 1971 (also translated into Russian in 1974)
  • with I. Niven, HS Zuckerman: Introduction to the theory of Numbers , Wiley, 5th edition 1991, ISBN 0-471-62546-9 (the previous volume by Niven, Zuckerman was first published in 1960 and also in German as a BI paperback in two volumes )
  • with Robert C. Vaughan: Multiplicative Number Theory , Volume 1, Classical Theory , Cambridge University Press 2006
  • Ten lectures on the interface between analytic number theory and harmonic analysis , American Mathematical Society, CBMS Vol. 84, 1994

Web links

References

  1. ↑ The pair correlation of zeros of the zeta function , in HG Diamond (ed.): Analytic number theory , Proceedings of Symposia in Pure Mathematics 24, AMS, Providence 1973, pp. 181-193
personal data
SURNAME Montgomery, Hugh
ALTERNATIVE NAMES Montgomery, Hugh Lowell (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH August 26, 1944
PLACE OF BIRTH Muncie , Indiana