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