Automorphic representations and applications

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半积分权值形式的问题，包括基于l值与半积分权值形式的傅里叶系数之间关系的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还将研究Gindikin-Karpelevich型公式，并研究它们在相对痕量公式中的应用。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。它是数学最古老的分支之一。在过去的半个世纪中，它已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 the proposal DMS-0700030 of MaoThis work concerns some problems in the theory of automorphic forms. The PI will use the theory of automorphic representations to study problems in half integral weight forms, including algorithm for L-values based on a relation between L-values and Fourier coefficients of half integral weight forms. The PI and others will investigate the generalization of this relation to L-values of automorphic forms on higher ranked groups. The PI will also look at Gindikin-Karpelevich type formulas and investigate their application in relative trace formula.This research is in the area of number theory. Number theory has its historical roots in the study of natural numbers. It is among the oldest branches of mathematics. Within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.