Abstract
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 $s=frac {1+i}{2}$.
Degree
MS
College and Department
Physical and Mathematical Sciences; Mathematics
Rights
http://lib.byu.edu/about/copyright/
BYU ScholarsArchive Citation
Belt, Dustin David, "Topics on the Spectral Theory of Automorphic Forms" (2006). Theses and Dissertations. 490.
https://scholarsarchive.byu.edu/etd/490
Date Submitted
2006-07-12
Document Type
Thesis
Handle
http://hdl.lib.byu.edu/1877/etd1423
Keywords
automorphic forms, Eisenstein series, Dirichlet series, Selberg's Eigenvalue Conjecture
Language
English