A note on a generalized circular summation formula of theta functions

DOI10.1016/j.jnt.2011.12.016zbMath1273.11075arXiv1202.1869OpenAlexW2964309967MaRDI QIDQ413418

Jun-Ming Zhu

Publication date: 7 May 2012

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

Full work available at URL: https://arxiv.org/abs/1202.1869

zbMATH Keywords

theta functioncircular summationcubic theta functionJacobi imaginary transformation

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Theta series; Weil representation; theta correspondences (11F27) Jacobi forms (11F50) Elliptic functions and integrals (33E05)

Related Items (7)

SOME INVERSE RELATIONS AND THETA FUNCTION IDENTITIES ⋮ Circular summation formulas for theta function \(\vartheta_4(z| \tau)\) ⋮ Some Ramanujan-type circular summation formulas ⋮ Some circular summation formulas for theta functions ⋮ 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

• Unnamed Item
• The products of three theta functions and the general cubic theta functions
• Circular summation of theta functions in Ramanujan's lost notebook
• On a new circular summation of theta functions
• A generalized circular summation of theta function and its application
• Unification of the cubic analogues of the Jacobian theta-function
• Cubic identities for theta series in three variables
• Additive decompositions of θ-functions of multiple arguments

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