This grant supports the research of Professor Roger Baker in analytic number theory. Professor Baker will study a broad class of problems in Diophantine inequalities around Weyl sums. He will also study exponential sums via the values of Dirichlet polynomials and sieves. 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.
