## Experimental Mathematics

### An Explicit Formula for the Arithmetic--Geometric Mean in Genus 3

#### Abstract

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 Richelot (1837) and Humbert (1901). We present the analogous algorithm for abelian integrals of genus 3.

#### Article information

Source
Experiment. Math., Volume 16, Issue 4 (2007), 421-440.

Dates
First available in Project Euclid: 6 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.em/1204836513

Mathematical Reviews number (MathSciNet)
MR2378484

Zentralblatt MATH identifier
1131.14038

#### Citation

Lehavi, D.; Ritzenthaler, C. An Explicit Formula for the Arithmetic--Geometric Mean in Genus 3. Experiment. Math. 16 (2007), no. 4, 421--440. https://projecteuclid.org/euclid.em/1204836513