A generalized circular summation of theta function and its application

DOI10.1016/j.jmaa.2009.03.047zbMath1213.11099OpenAlexW2027685167MaRDI QIDQ1025051

Xian-Feng Zeng

Publication date: 18 June 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.03.047

zbMATH Keywords

theta functionelliptic functioncircular summation

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27)

Related Items (11)

Circular summation formulas for theta function \(\vartheta_4(z| \tau)\) ⋮ Some Ramanujan-type circular summation formulas ⋮ A theta function identity and its applications ⋮ A note on a generalized circular summation formula of theta functions ⋮ An elementary proof of Ramanujan's circular summation formula and its generalizations ⋮ Some circular summation formulas for theta functions ⋮ The \(t\)-coefficient method. III: A general series expansion for the product of theta functions with different bases and its applications. ⋮ Some new circular summation formulas of theta functions ⋮ On a new circular summation of theta functions ⋮ Some extensions for Ramanujan's circular summation formulas and applications ⋮ A note for Ramanujan's circular summation formula

Cites Work

• Unnamed Item
• Circular summation of theta functions in Ramanujan's lost notebook
• Additive decompositions of θ-functions of multiple arguments
• Cubic Analogues of the Jacobian Theta Function θ(z, q)
• On the Additive Formulae of the Theta Functions and a Collection of Lambert Series Pertaining to the Modular Equations of Degree 5

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