Automorphic representations and applications

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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.