On the theory of elliptic functions based on ₂𝐹₁(\frac{1}3,\frac{2}3;\frac{1}2;𝑧)

DOI10.1090/S0002-9947-04-03600-1zbMath1145.11321OpenAlexW1508899516MaRDI QIDQ4654097

Li-Chien Shen

Publication date: 1 March 2005

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-04-03600-1

zbMATH Keywords

theta functionsJacobian elliptic functionscubic theory of elliptic functionsWeierstrass \(\wp \) function

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Gauss and Kloosterman sums; generalizations (11L05) Holomorphic modular forms of integral weight (11F11) Elliptic functions and integrals (33E05)

Related Items (4)

On Hecke groups, Schwarzian triangle functions and a class of hyper-elliptic functions ⋮ An addition formula for the Jacobian theta function and its applications ⋮ Cubic theta functions ⋮ Quantum geometry of resurgent perturbative/nonperturbative relations

Cites Work

• Unnamed Item
• On an identity of Ramanujan based on the hypergeometric series \(_2F_1(\frac{1}{3},\frac{2}{3};\frac{1}{2};x)\)
• On the Modular Equations of Degree 3
• A Cubic Counterpart of Jacobi's Identity and the AGM

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