Formulas for the arithmetic geometric mean of curves of genus 3

Abstract

The arithmetic geometric mean algorithm for calculation of elliptic integrals of the first type was introduced by Gauss. The analog algorithm for Abelian integrals of genus 2 was introduced by Richelot (1837) and Humbert (1901). We present the analogous algorithm for Abelian integrals of genus 3.

26 pages, amslatex, xypic +2 eps figures

References in corpus (1)

• The arithmetic-geometric mean and isogenies for curves of higher genus

Cited by in corpus (2)

• Effective reconstruction of generic genus 4 curves from their theta hyperplanes
• Computing isogenies between Jacobian of curves of genus 2 and 3