Cubic theta functions.

DOI10.1016/S0377-0427(03)00614-9zbMath1107.33022MaRDI QIDQ1414328

Shaun Cooper

Publication date: 20 November 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Dedekind eta functioncubic theta functionsmodular transformation

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Dedekind eta function, Dedekind sums (11F20) Elliptic functions and integrals (33E05)

Related Items (10)

Cubic elliptic functions ⋮ A simple proof of an expansion of an eta-quotient as a Lambert series ⋮ The products of three theta functions and the general cubic theta functions ⋮ Explicit evaluations of cubic and quartic theta-functions ⋮ Determinant identities for theta functions ⋮ The \(t\)-coefficient method. III: A general series expansion for the product of theta functions with different bases and its applications. ⋮ Supersingular parameters of the Deuring normal form ⋮ Sixteen Eisenstein series ⋮ Magic determinants of Somos sequences and theta functions ⋮ On Ramanujan's general theta function and a generalization of the Borweins' cubic theta functions

Cites Work

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• Unification of the cubic analogues of the Jacobian theta-function
• Cubic Analogues of the Jacobian Theta Function θ(z, q)
• Some Cubic Modular Identities of Ramanujan
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• A Cubic Counterpart of Jacobi's Identity and the AGM

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