Thomae's Derivative Formulae for Trigonal Curves

TL;DR

This paper establishes a Thomae derivative formula for trigonal curves with non-singular affine models, linking derivatives of theta functions to explicit branching value expressions.

Contribution

It introduces a new Thomae derivative formula specifically for trigonal curves with non-singular affine models, expanding the theoretical understanding of theta functions.

Findings

Derived explicit formulas relating theta function derivatives to branching values.

Extended Thomae's classical formulas to a broader class of trigonal curves.

Provided mathematical tools for analyzing trigonal curve properties.

Abstract

In this paper we prove a Thomae derivative formula for trigonal curves admitting a non-singular affine model. This formula relates the derivatives of theta functions with rational characteristics on the curve to explicit expressions in the branching values.