Quadratic iterations to ${\pi }$ associated with elliptic functions to the cubic and septic base

DOI10.1090/S0002-9947-02-03192-6zbMath1021.11036MaRDI QIDQ4787471

Kok Seng Chua, Heng Huat Chan, Patrick Solé

Publication date: 7 January 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

modular functionselliptic functionsJacobi theta functionsPi

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05) Evaluation of number-theoretic constants (11Y60)

Related Items (5)

Codes over $\mathbf {GF\pmb (4\pmb )}$ and $\mathbf {F}_2 \times \mathbf {F}_2$ and Hermitian lattices over imaginary quadratic fields ⋮ Lattices in real quadratic fields and associated theta series arising from codes over \({\mathbb{F}}_4\) and \({\mathbb{F}}_2 \times {\mathbb{F}}_2\) ⋮ Eisenstein lattices, Galois rings, and theta series. ⋮ Broué-Enguehard maps and Atkin-Lehner involutions ⋮ Jacobi identities, modular lattices, and modular towers

Cites Work

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• Hypergeometric analogues of the arithmetic-geometric mean iteration
• Seven-modular lattices and a septic base Jacobi identity.
• [https://portal.mardi4nfdi.de/wiki/Publication:3829784 On the Mean Iteration (a, b) ← � � a+3b 4 , √ab+b 2 � �]
• On Ramanujan's cubic transformation formula for 2 F 1(1/3, 2/3; 1; z)
• On Eisenstein series and ∑_{𝑚,𝑛=-∞}^{∞}𝑞^{𝑚²+𝑚𝑛+2𝑛²}
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• A Cubic Counterpart of Jacobi's Identity and the AGM

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