On quintic identities

TL;DR

This paper derives quintic analogs of classical cubic identities and explores the algebraic structure of theta constants at level five, suggesting potential generalizations to higher powers.

Contribution

It introduces quintic versions of Farkas and Kra identities and analyzes the algebraic structure of theta constants of level five, extending previous cubic results.

Findings

Derived quintic identities analogous to cubic ones

Analyzed algebraic structure of theta constants at level five

Proposed generalization to higher powers

Abstract

In this paper, we derive quintic versions of the cubic identities of Farkas and Kra. We believe that our results can be easily generalized to $k$ th power versions,$(k=7,9,11,\ldots).$ Moreover, we investigate the algebraic structure of theta constants of level five.