A JACOBI-TYPE FORMULA FOR A FAMILY OF HYPERELLIPTIC CURVES OF GENUS 3 WITH AUTOMORPHISM OF ORDER 4
A JACOBI-TYPE FORMULA FOR A FAMILY OF HYPERELLIPTIC CURVES OF GENUS 3 WITH AUTOMORPHISM OF ORDER 4
In this paper we show a two-dimensional variant of the classical Jacobi formula between a theta constant and the Gauss hypergeometric function. We use the family of algebraic curves given in the form w4 = z2(z-1)2(z-λ1)(z-λ2) with two complex parameters λ1,λ2 and the modular functions for them. Our result is …