An analogy of Jacobi's formula and its applications

DOI10.14492/hokmj/2021-572arXiv2202.11856MaRDI QIDQ6185377

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Publication date: 8 January 2024

Published in: Hokkaido Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.11856

zbMATH Keywords

hypergeometric functiontheta constantsmean iteration

Mathematics Subject Classification ID

Theta functions and abelian varieties (14K25) Classical hypergeometric functions, ({}_2F_1) (33C05) Numerical approximation and evaluation of special functions (33F05) Evaluation of number-theoretic constants (11Y60)

Cites Work

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• Mean iterations derived from transformation formulas for the hypergeometric function
• Isogeny formulas for the Picard modular form and a three terms arithmetic geometric mean
• An extended Gauss AGM and corresponding Picard modular forms
• A transformation formula for Appell's hypergeometric function \(F_1\) and common limits of triple sequences by mean iterations
• Schwarz's map for Appell's second hypergeometric system with quarter integer parameters
• A variant of Jacobi type formula for Picard curves
• Thomae type formula for K3 surfaces given by double covers of the projective plane branching along six lines
• A JACOBI-TYPE FORMULA FOR A FAMILY OF HYPERELLIPTIC CURVES OF GENUS 3 WITH AUTOMORPHISM OF ORDER 4
• Functional Equations for Appell's <i>F</i>₁ Arising from Transformations of Elliptic Curves

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