On theta functions of order four

TL;DR

This paper proves that the fourth powers of even theta functions form a basis for the space of even theta functions of order four on certain Abelian varieties, under specific conditions.

Contribution

It establishes a basis for even theta functions of order four using fourth powers of theta functions with even characteristics, expanding understanding of their structure.

Findings

Fourth powers of even theta functions form a basis.

Basis applies to Abelian varieties without vanishing theta-null.

Provides a new structural insight into theta functions.

Abstract

We prove that the fourth powers of theta functions with even characteristics form a basis of the space of even theta functions of order four on a principally polarized Abelian variety without vanishing theta-null.