Topics on the Spectral Theory of Automorphic Forms

We study the analytic properties of the Eisenstein Series of $frac {1}{2}$-integral weight associated with the Hecke congruence subgroup Gamma₀(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 Gamma₀(N) at $s=frac {1+i}{2}$.

Name thesis:degree_name

MS

Grantor dc:publisher

Brigham Young University - Provo

Author dc:creator

• Belt, Dustin David

• automorphic forms
• Eisenstein series
• Dirichlet series
• Selberg's Eigenvalue Conjecture
• Mathematics

Language dc:language

English

Repository record dc:identifier

https://scholarsarchive.byu.edu/etd/490

OAI identifier oai:identifier

oai:scholarsarchive.byu.edu:etd-1489