Elliptic Zeta Functions

Abstract

The main goal of this thesis is to develop and study the theory of the so-called elliptic zeta functions. These are functions on $\CC\times {\mathcal L}$, where $\mathcal L$ is the set of rank 2 lattices in the complex plane, satisfying a quasi-periodicity with respect to the first factor and a certain modular invariance property with respect to the second factor. The prototype is the Weierstrass zeta $\zeta-$function. We show how these elliptic zeta functions are closely connected to modular forms and to the theory of equivariant functions.