On a new circular summation of theta functions

DOI10.1016/j.jnt.2009.09.011zbMath1196.33016OpenAlexW1968413824MaRDI QIDQ971847

Zhi-Guo Liu, Song Heng Chan

Publication date: 17 May 2010

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2009.09.011

zbMATH Keywords

theta functionmodular equationelliptic functionaddition formulacircular summation

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Holomorphic modular forms of integral weight (11F11) Dedekind eta function, Dedekind sums (11F20) Elliptic functions and integrals (33E05)

Related Items (11)

SOME INVERSE RELATIONS AND THETA FUNCTION IDENTITIES ⋮ 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 ⋮ 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
• A generalized circular summation of theta function and its application
• On the circular summation of the eleventh powers of Ramanujan's theta function
• On a result of Ramanujan on theta functions
• Circular summation of the 13th powers of Ramanujan's theta function
• Circular summations of theta functions in Ramanujan's lost notebook
• Unification of the cubic analogues of the Jacobian theta-function
• The root lattice $A^*_n$ and Ramanujan’s circular summation of theta functions
• Additive decompositions of θ-functions of multiple arguments
• Cubic Analogues of the Jacobian Theta Function θ(z, q)
• Some Cubic Modular Identities of Ramanujan
• The sixth, eighth, ninth, and tenth powers of Ramanujan’s theta function
• A Cubic Counterpart of Jacobi's Identity and the AGM

This page was built for publication: On a new circular summation of theta functions