Hugh Montgomery (mathematician)

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

Life and work

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

Montgomery discovered pair correlations of zeros of the Riemann zeta function, which, as it resulted 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. The result is a novel approach to the study of the Riemann zeta function and other zeta functions of mathematics. He also dealt with the method of the Great sieve.

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

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.

His doctoral counts Brian Conrey.

Writings

• Topics in multiplicative number theory, Springer, Lecture Notes in Mathematics 227, 1971 ( also translated into Russian 1974)
• With Robert C. Vaughan: Multiplicative Number Theory, Volume 1, Classical Theory, Cambridge University Press 2006
• Ten lectures on the interface in between analytic number theory and harmonic analysis, American Mathematical Society, CBMS Bd.84, 1994