Hyperelliptic integrals and generalized arithmetic-geometric mean

DOI10.1007/s11139-011-9353-7zbMath1260.14053OpenAlexW2076738479MaRDI QIDQ452260

Duco van Straten, Jeroen G. Spandaw

Publication date: 20 September 2012

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-011-9353-7

zbMATH Keywords

theta functionshyperelliptic integralsarithmetic-geometric means

Mathematics Subject Classification ID

Jacobians, Prym varieties (14H40) Theta functions and abelian varieties (14K25) Theta series; Weil representation; theta correspondences (11F27) Special sequences and polynomials (11B83)

Related Items (2)

Parametrized means and limit properties of their Gaussian iterations ⋮ The AM-GM inequality from different viewpoints

Cites Work

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• Higher genus arithmetic-geometric means
• The arithmetic-geometric mean of Gauss
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Theta functions on Riemann surfaces
• Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses, π, and the Ladies Diary
• The arithmetic-geometric mean and isogenies for curves of higher genus
• An Explicit Formula for the Arithmetic–Geometric Mean in Genus 3
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura

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