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.Mathematic
