Modular equations of order $p$ and Theta functions

TL;DR

This paper introduces an algorithm to derive modular equations relating theta functions evaluated at  and p for higher genus, expanding tools for understanding complex multiplication and modular forms.

Contribution

It presents a novel algorithm for deriving modular equations between theta functions at  and p for genus greater than one.

Findings

Provides a systematic method for obtaining modular equations.

Enhances understanding of theta functions in higher genus cases.

Facilitates computations involving modular forms.

Abstract

An algorithm to obtain equations between theta functions with integral characteristics evaluated at $\tau$ and $p\tau$ for $g>1$ is presented.