Alshbeil, Isra2020-06-092020-06-092020-06-09http://hdl.handle.net/10393/40609http://dx.doi.org/10.20381/ruor-24837The 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.enEquivariant FunctionsModular FormQuasiperiod mapThesis