Mathematical Sciences: Automorphic Forms and Representation Theory

本文研究自守形式 和使用几何方法的表示理论。 主要 问题是获得解析延拓和泛函 Shimura品种的Hasse-Weil zeta函数方程。 其目的是用以下形式表达这些zeta函数： 自守L-函数 那么就必须得到 这些自守L函数的定律。 本研究将研究的生成函数， 多项式方程组的解的个数 超级英雄 这些函数的性质将给出一个 大量的关于解决问题的信息， Diophantine Equations（丢番图方程） 数论作为 它的主要组成部分之一，丢番图方程的研究， 也就是整数方程组的解

This research deals with the subject of automorphic forms and representation theory using geometric methods. The main problem is to obtain the analytic continuation and functional equation of the Hasse-Weil zeta function of Shimura varieties. The object is to express these zeta functions in terms of automorphic L-functions. Then one must obtain the transformation laws for these automorphic L-functions. This research will study the generating functions for the number of solutions of systems of polynomial equations modulo all the primes. The properties of these functions will give an immense amount of information concerning the solution to the corresponding set of Diophantine Equations. Number Theory has as one of its chief components the study of Diophantine Equations, that is the solution of sets of equations in integers.