Mathematical Sciences: L-functions, Exponential Sums, and Applications of Automorphic Theory to Diophantine Problems

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This grant supports the research of Professor H. Iwaniec and W. Duke to work on several problems connected with analytic number theory and automorphic forms. In particular, they will attempt to establish analytic continuation of L-functions derived from the product of two L-functions which have functional equations. They will also attempt to establish the equidistribution of roots of quadratic congruences to prime module and finally they will study generalization of the Linnik problem about lattice points in family of varieties. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.