On Hecke groups, Schwarzian triangle functions and a class of hyper-elliptic functions

DOI10.1007/s11139-015-9747-zzbMath1337.33010OpenAlexW2285764476MaRDI QIDQ265594

Li-Chien Shen

Publication date: 4 April 2016

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

Full work available at URL: https://doi.org/10.1007/s11139-015-9747-z

zbMATH Keywords

Eisenstein seriesHecke groupshypergeometric functionJacobi theta functionshyperelliptic functionsLegendre functionSchwarzian triangle function

Mathematics Subject Classification ID

Theta functions and abelian varieties (14K25) Elliptic integrals as hypergeometric functions (33C75)

Related Items (3)

On Schwarzian triangle functions, automorphic forms and a generalization of Ramanujan's triple differential equations ⋮ Quantum geometry of resurgent perturbative/nonperturbative relations ⋮ Aspects of Hecke symmetry: anomalies, curves, and chazy equations

Cites Work

• On a theory of elliptic functions based on the incomplete integral of the hypergeometric function \({_{2}}F_{1}(\frac{1}{4},\frac{3}{4};\frac{1}{2};z)\)
• Nonlinear differential equations satisfied by certain classical modular forms
• Domb's numbers and Ramanujan-Sato type series for \(1/\pi\)
• A note on the Schwarzian triangle functions
• On the theory of elliptic functions based on ₂𝐹₁(\frac{1}3,\frac{2}3;\frac{1}2;𝑧)
• A Cubic Counterpart of Jacobi's Identity and the AGM
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