A new proof of a Thomae-like formula for non hyperelliptic genus 3 curves
Enric Nart, Christophe Ritzenthaler
TL;DR
This paper presents a new proof of a Thomae-like formula for non-hyperelliptic genus 3 curves, connecting Weber's formula with the Riemann-Jacobi formula to simplify derivation.
Contribution
It provides a novel, simplified proof of a classical formula relating theta constants and bitangents for genus 3 curves.
Findings
Weber's formula can be derived from the Riemann-Jacobi formula.
The proof simplifies understanding of theta constants for non-hyperelliptic genus 3 curves.
The approach clarifies the relationship between bitangents and theta null values.
Abstract
We discuss Weber's formula which gives the quotient of two Thetanullwerte for a plane smooth quartic in terms of the bitangents. In particular, we show how it can easily be derived from the Riemann-Jacobi formula.
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