Topics in Automorphic Form

本文讨论了自同构形理论中的几个问题。该PI将利用自同构表示的理论来研究计算数论问题，并根据L值与半整数权形式的傅立叶系数之间的关系，发展出一种求L值的算法。PI和其他人将研究这种关系对高阶群上自同构形的L值的推广。PI将与S.Rallis一起继续发展相对论公式的理论。数论起源于对自然数的研究。它是数学中最古老的分支之一。在过去的半个世纪里，它已经成为数据传输和处理以及通信系统等领域的各种应用中不可或缺的工具。

Abstract for award DMS-0355285 of MaoThis work concerns some problems in the theory of automorphic forms. ThePI will use the theory of automorphic representations to study acomputational number theory problem, and develop an algorithm for L-valuesbased on a relation between L-values and Fourier coefficients of halfintegral weight forms. The PI and others will investigate thegeneralization of this relation to L-values of automorphic forms on higherranked groups. The PI will continue development of the theory of relativetrace formula with S. Rallis.This research is in the area of number theory. Number theory has itshistorical roots in the study of natural numbers. It is among the oldestbranches of mathematics. Within the last half century it has become anindispensible tool in diverse applications in areas such as datatransmission and processing, and communication systems.