Topics in Automorphic Form

本文涉及自同构形式理论中的一些问题。pi将使用自同构表示理论来研究计算数论问题，并基于l值与半积分权重形式的傅立叶系数之间的关系开发l值算法。PI和其他人将研究这个关系推广到高阶群上自同构形式的l值。PI将与S. Rallis一起继续发展相对轨迹公式理论。这项研究属于数论领域。数论的历史根源在于对自然数的研究。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各种应用领域不可或缺的工具。

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.