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

这笔赠款支持H.Iwaniec教授和W.Duke教授研究与解析数论和自同构形式有关的几个问题。特别地，他们将尝试建立由两个具有函数方程的L函数的乘积导出的L函数的解析延拓。他们还将尝试建立素模的二次同余根的等分布，最后他们将研究关于格点的Linnik问题在变种族中的推广。这是数论领域的研究。数论始于整数和诸如一个整数被另一个整数整除的问题。它是最古老的数学领域之一，最初是出于纯粹的美学原因。然而，在过去的半个世纪里，它已经成为开发计算机科学的新算法和电子产品的新纠错码的必要工具。

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.