Mathematical Sciences: Convolution Orthogonality

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This grant supports the research of Professor B. Smith to work on general Tauberian theorems and their applications to number theory. In particular, he wishes to develop a Tauberian theorem that would be applicable to the estimation of integrals that arise in the twin prime conjecture. The field of analytic number theory applies to the discrete realm of the whole numbers the techniques of analysis. These techniques, dependent on the notions of continuity and limit, originated with the 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.