Topics in Automorphic Form

本文涉及自守型理论中的一些问题。PI将使用自守表示理论来研究计算数论问题，并基于L值与半整数权形式的傅立叶系数之间的关系来开发L值的算法。PI和其他人将研究这种关系的推广到更高等级群上自守形式的L值。PI将继续发展与S.拉利斯。这项研究是在数论领域。数论在历史上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，它已成为一个不可或缺的工具，在不同的应用领域，如数据传输和处理，通信系统。

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.