Formulas for the arithmetic geometric mean of curves of genus 3
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- March 2004
- DOI:
- 10.48550/arXiv.math/0403182
- arXiv:
- arXiv:math/0403182
- Bibcode:
- 2004math......3182L
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14H40;
- 14H45;
- 14Q05
- E-Print:
- 26 pages, amslatex, xypic +2 eps figures