The Kronecker theta function and a decomposition theorem for theta functions. I

DOI10.1007/s11139-020-00376-6zbMath1529.11067arXiv2012.01670OpenAlexW3128719367MaRDI QIDQ6158140

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Publication date: 31 May 2023

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

Full work available at URL: https://arxiv.org/abs/2012.01670

zbMATH Keywords

theta functionelliptic functionKronecker theta functionRamanujan \({}_1 \psi_1\) summation

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Theta series; Weil representation; theta correspondences (11F27) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Cites Work

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• A simple proof of Ramanujan's summation of the \(_1\Psi_1\)
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• On the equivalence of two fundamental theta identities
• SOME INVERSE RELATIONS AND THETA FUNCTION IDENTITIES
• Shorter Notes: A Simple Proof of Ramanujan's 1 Ψ 1 Sum
• On the Additive Formulae of the Theta Functions and a Collection of Lambert Series Pertaining to the Modular Equations of Degree 5
• On the Modular Equations of Degree 3
• On the trigonometric expansion of elliptic functions
• An elementary proof of p(11m+6)≡0 (mod 11)
• NOTE ON SOME PARTITION FORMULAE
• Residue theorem and theta function identities

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