A new proof of a Thomae-like formula for non hyperelliptic genus 3 curves

Enric Nart (1) , Christophe Ritzenthaler (2)

1 UAB - Universitat Autònoma de Barcelona = Autonomous University of Barcelona = Universidad Autónoma de Barcelona
2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Domaines: Géométrie algébrique [math.AG]

Enric Nart, Christophe Ritzenthaler. A new proof of a Thomae-like formula for non hyperelliptic genus 3 curves. Alp Bassa; Alain Couvreur; David Kohel. Arithmetic, geometry, cryptography and coding theory, 686, American Mathematical Society, pp.137-155, 2017, Contemporary Mathematics, 978-1-4704-2810-5. ⟨hal-01128237⟩