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Formulas for the arithmetic geometric mean of curves of genus 3

D. Lehavi·C. Ritzenthaler
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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.

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D. Lehavi, C. Ritzenthaler. 2005-12-20. Formulas for the arithmetic geometric mean of curves of genus 3. https://doi.org/10.1080/10586458.2007.10129011

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