SOME INVERSE RELATIONS AND THETA FUNCTION IDENTITIES

DOI10.1142/S1793042112501126zbMath1272.11060OpenAlexW2135858088MaRDI QIDQ3165312

Zhi-Guo Liu

Publication date: 26 October 2012

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042112501126

zbMATH Keywords

entire functiontheta functionFourier serieselliptic functionSchröter formula

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Theta series; Weil representation; theta correspondences (11F27) Elliptic functions and integrals (33E05)

Related Items (10)

Circular summation formulas for theta function \(\vartheta_4(z| \tau)\) ⋮ Some Ramanujan-type circular summation formulas ⋮ Discrete Fourier Transform and Theta Function Identities ⋮ The Kronecker theta function and a decomposition theorem for theta functions. I ⋮ Some circular summation formulas for theta functions ⋮ Spontaneous staggered polarizations of the cyclic solid-on-solid model from the algebraic Bethe Ansatz ⋮ Multi-point local height probabilities of the CSOS model within the algebraic Bethe ansatz framework ⋮ Some new circular summation formulas of theta functions ⋮ Some extensions for Ramanujan's circular summation formulas and applications ⋮ A note for Ramanujan's circular summation formula

Cites Work

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• The products of three theta functions and the general cubic theta functions
• Circular summation of theta functions in Ramanujan's lost notebook
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• Theta function identities
• On a new circular summation of theta functions
• An extension of the quintuple product identity and its applications
• On an identity of Ramanujan based on the hypergeometric series \(_2F_1(\frac{1}{3},\frac{2}{3};\frac{1}{2};x)\)
• A new proof of Windquist's identity
• Uniform proofs of \(q\)-series-product identities
• On the products of three theta functions
• Another simple proof of the quintuple product identity
• Verification method for theta function identities via Liouville's theorem
• A three-term theta function identity and its applications
• On a combinatorial identity of Winquist and its generalization
• Additive decompositions of θ-functions of multiple arguments
• ON THE SCHRÖTER FORMULA FOR THETA FUNCTIONS
• Applications of Basic Hypergeometric Functions
• On the quintuple product identity
• A theta function identity and its implications
• THE QUINTUPLE PRODUCT IDENTITY
• An elementary proof of p(11m+6)≡0 (mod 11)

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