# Elliptic Zeta functions and equivariant functions,

## TL;DR

This paper explores the relationships between modular forms, equivariant functions, and elliptic zeta functions, revealing how these mathematical objects are interconnected and can be parameterized by each other.

## Contribution

It establishes a novel connection linking weight two meromorphic modular forms, equivariant functions, and elliptic zeta functions associated with a modular subgroup.

## Key findings

- Equivariant functions can be parameterized by modular objects.
- Elliptic zeta functions generalize Weierstrass zeta functions.
- A close relationship between the three notions is demonstrated.

## Abstract

In this paper we establish a close connection between three notions at- tached to a modular subgroup. Namely the set of weight two meromorphic modular forms, the set of equivariant functions on the upper half-plane commuting with the action of the modular subgroup and the set of elliptic zeta functions generalizing the Weierstrass zeta functions. In particular, we show that the equivariant functions can be parameterized by modular objects as well as by elliptic objects.