Faculty

Biography

Professor Gonek received his BS with Highest Honors in Mathematics in 1973, an MS in Mathematics in 1976, and a PhD in Mathematics in 1979, all from the University of Michigan. After a two-year position at Temple University from 1978 to 1980, he joined the University of Rochester as an Assistant Professor of Mathematics in 1980 and is now a Full Professor. He spent the 1984-85 academic year at Oklahoma State University, part of Fall 1991 at Macquarie University in Sydney, Australia, part of Fall 1999 at the American Institute of Mathematics in Palo Alto, and half of 2004 at the Newton Institute in Cambridge, England.

Research Overview

Professor Gonek’s research interests are in the field of analytic number theory, particularly multiplicative number theory, the theory of the Riemann zeta-function, L-functions, and the distribution of prime numbers. Some of his work has focused on moments of the Riemann zeta-function, discrete mean value theorems for the zeta-function and L-functions, and the development and application of random matrix models for the zeta-function. One goal of this work is to better understand the behavior (the distribution of zeros, maximal order, and so on) of the zeta and L-functions themselves. Another is to determine connections between these behaviors and various arithmetical problems. Professor Gonek has also worked on questions relating to the distribution of multiplicative inverses and primitive roots in residue classes modulo a prime.

Research Interests

• Multiplicative number theory
• Theory of the Riemann zeta-function
• L-functions
• Distribution of prime numbers

Selected Publications

• Truncated Product Representations for L-Functions in the Hyperelliptic Ensemble (with J. C. Andrade and J. P. Keating)
• The θ=∞θ=∞ conjecture implies the Riemann hypothesis, with Sandro Bettin
• On the distribution of positive and negative values of Hardy’s ZZ-function, with A. Ivic
• A hybrid Euler-Hadamard product for the Riemann zeta function, with C. P. Hughes and J. P. Keating
• Simple zeros of zeta functions, with B. Conrey and A. Ghosh
• A formula of Landau and mean values of zeta(s)
• On the distribution of gaps between zeros of the zeta-function, with J. B. Conrey and A. Ghosh
• Simple zeros of the Riemann zeta-function, with J. B. Conrey and A. Ghosh
• A note on gaps between zeros of the zeta function, with J. B. Conrey and A. Ghosh
• Mean values of the Riemann zeta-function and its derivatives
• The zeros of Hurwitz’s zeta-function on σ=1/2
• A note on Turan’s Method
• Analytic properties of zeta and LL-functions: Thesis, Part 1
• Thesis, Part 2
• Thesis, Part 3
• Thesis, Part 4
• On extensions of an inequality among means, with F. Chan and D. Goldberg

Teaching

Professor Gonek has been involved with many aspects of teaching at Rochester. In the early nineties he designed and ran a mathematics camp for bright mathematics majors from various colleges, he introduced the workshop idea into mathematics courses at Rochester, he led a committee to examine and reform the undergraduate curriculum, and he helped design a number of the College’s “Quest” courses. He recently developed and taught an interdisciplinary Quest course with a colleague from the department of Religion and Classics called “The Infinite”. In 1998 Professor Gonek won a Goergen Award for Distinguished Achievement and Artistry in Undergraduate Teaching.