This award supports the research in analytic number theory of Professor Daniel Goldston of San Jose State University. Dr. Goldston's project involves a study of the fine details in the pattern of distribution of prime numbers. He plans to examine the Hardy-Littlewood circle method and its application to the study of small gaps between primes and the exceptional sets for the Goldbach conjecture; the Riemann zeta function as a tool for studying large gaps between primes; Maier's method and differential delay questions; and connections of these methods with the emerging understanding of the duality between primes and zeros of zeta functions. The field of analytic number theory applies to the discrete realm of the whole numbers the techniques of analysis, dependent on the notions of continuity and limit, originating in calculus. The idea of using continuous methods to investigate the discrete is two centuries old, but with the work of the modern analytic number theorists such as Professor Goldston, the field has had a new rebirth.
