Some applications of classical modular forms to number theory

Access full-text files

Date

2005

Authors

Masri, Riad Mohamad

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

In this thesis we use classical modular forms to study several problems in number theory. In chapter 2 we use non-holomorphic Eisenstein series for the Hilbert modular group to obtain a formula for the relative class number of certain abelian extensions of CM number fields. In chapter 3 we compute the scattering determinant for the Hilbert modular group, and explain how this can be used to prove that the subspace of cuspidal, square integrable eigenfunctions for the Laplacian on products of rank one symmetric spaces is infinite dimensional. In chapter 4 we use zeta functions of quadratic forms over number fields to sharpen a certain constant appearing in C. L. Siegel’s lower bound for the residue of the Dedekind zeta function at s = 1.

Department

Description

Keywords

LCSH Subject Headings

Citation