Modular forms from the Weierstrass functions

TL;DR

This paper constructs specific elliptic modular forms of weights 1 and 2 using Weierstrass functions and evaluates their values at certain cusps, contributing to the understanding of modular forms via classical functions.

Contribution

It introduces a novel method of constructing modular forms from Weierstrass functions and computes their values at cusps, expanding classical approaches.

Findings

Constructed weight 2 and weight 1 modular forms from Weierstrass functions.

Calculated the values of these modular forms at specific cusps.

Demonstrated the effectiveness of Weierstrass functions in modular form construction.

Abstract

We construct holomorphic elliptic modular forms of weight 2 and weight 1, by special values of Weierstrass p-functions, and by differences of special values of Weierstrass zeta-functions, respectively. Also we calculated the values of these forms at some cusps.