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

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