Mathematical Sciences: RUI: Binary Additive Problems Involving Primes and Other Topics in Analytic Number Theory

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This grant supports the research of Professor Daniel Goldston in analytic number theory. Professor Goldston will use a new approximation to the von Mangoldt lambda function to study problems that were previously examined with the circle method. He will also study pair correlations of the zeros of zeta functions and Siegel zeros. 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, the field has had a new rebirth.