An explicit formula for the arithmetic-geometric mean in genus 3. (English) Zbl 1131.14038

Lehavi, D.; Ritzenthaler, C.

Exp. Math. 16, No. 4, 421-440 (2007).

Summary: The arithmetic-geometric mean algorithm for calculating elliptic integrals of the first type was introduced by Gauss. The analogous algorithm for abelian integrals of genus 2 was introduced by F. Richelot [J. Reine Angew. Math. 16, 221–341 (1837; ERAM 016.0545cj)] and G. Humbert [Journ. de Math. (5) 7, 359–417 (1901; JFM 32.0456.04)]. We present the analogous algorithm for abelian integrals of genus 3.

MSC:

14H40	Jacobians, Prym varieties
14H45	Special algebraic curves and curves of low genus
14Q05	Computational aspects of algebraic curves

Keywords:

Prym varieties; arithmetic geometric mean

Citations:

JFM 32.0456.04; ERAM 016.0545cj