Formulas for the arithmetic geometric mean of curves of genus 3

Details Formulas for the arithmetic geometric mean of curves of genus 3 Formulas for the arithmetic geometric mean of curves of genus 3

2004-03-10

arxiv.org/abs/math/0403182v2

Experimental Math. volume 16 (2007) issue 4. 421 - 440

Mathematics

Algebraic Geometry

26 pages, amslatex, xypic +2 eps figures

Scientific paper

10.1080/10586458.2007.10129011

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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