## Experimental Mathematics

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

### 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

**Subjects**

Primary: 14H40: Jacobians, Prym varieties [See also 32G20] 14H45: Special curves and curves of low genus 14Q05: Curves

**Keywords**

Prym varieties arithmetic geometric mean

#### 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