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Topics on the Spectral Theory of Automorphic Forms Topics on the Spectral Theory of Automorphic Forms

by Belt, Dustin David

Abstract (Summary)
We study the analytic properties of the Eisenstein Series of $frac {1}{2}$-integral weight associated with the Hecke congruence subgroup $Gamma_0(4)$. Using these properties we obtain asymptotics for sums of certain Dirichlet $L$-series. We also obtain a formula reducing the study of Selberg's Eigenvalue Conjecture to the study of the nonvanishing of the Eisenstein Series $E(z,s)$ for Hecke congruence subgroups $Gamma_0(N)$ at $s=frac {1+i}{2}$.
Bibliographical Information:

Advisor:

School:Brigham Young University

School Location:USA - Utah

Source Type:Master's Thesis

Keywords:automorphic forms eisenstein series dirichlet selberg s eigenvalue conjecture

ISBN:

Date of Publication:07/05/2006

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