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2007 An Explicit Formula for the Arithmetic--Geometric Mean in Genus 3
D. Lehavi, C. Ritzenthaler
Experiment. Math. 16(4): 421-440 (2007).

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.

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D. Lehavi. C. Ritzenthaler. "An Explicit Formula for the Arithmetic--Geometric Mean in Genus 3." Experiment. Math. 16 (4) 421 - 440, 2007.

Information

Published: 2007
First available in Project Euclid: 6 March 2008

zbMATH: 1131.14038
MathSciNet: MR2378484

Subjects:
Primary: 14H40 , 14H45 , 14Q05

Keywords: arithmetic geometric mean , Prym varieties

Rights: Copyright © 2007 A K Peters, Ltd.

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Vol.16 • No. 4 • 2007
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