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

该基金支持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。特别是，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。他们还将尝试建立二次同余到素数模的根的等分布，最后他们将研究关于变族中格点的Linnik问题的推广。这是数论领域的研究。数论从整数和诸如整数能被整数整除之类的问题开始。它是数学中最古老的领域之一，最初纯粹出于审美原因而追求它。然而，在过去的半个世纪里，它已经成为开发计算机科学新算法和电子学新纠错码的重要工具。

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.