Circular summation of theta functions in Ramanujan's lost notebook

DOI10.1016/j.jmaa.2005.05.015zbMath1129.33006OpenAlexW2078450633MaRDI QIDQ819739

Zhi-Guo Liu, Heng Huat Chan, Say Tiong Ng

Publication date: 29 March 2006

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.2005.05.015

zbMATH Keywords

theta functionsJacobi elliptic functionscircular summation

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items

SOME INVERSE RELATIONS AND THETA FUNCTION IDENTITIES ⋮ Circular summation formulas for theta function \(\vartheta_4(z| \tau)\) ⋮ Some Ramanujan-type circular summation formulas ⋮ 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 ⋮ 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 generalized circular summation of theta function and its application ⋮ Some identities for the partition function ⋮ Ramanujan's circular summation, \(t\)-cores and twisted partition identities ⋮ A note for Ramanujan's circular summation formula

Cites Work

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• On an identity of Ramanujan based on the hypergeometric series \(_2F_1(\frac{1}{3},\frac{2}{3};\frac{1}{2};x)\)
• 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
• New Ramanujan-Kolberg type partition identities.
• The root lattice $A^*_n$ and Ramanujan’s circular summation of theta functions
• A theta function identity and its implications
• The sixth, eighth, ninth, and tenth powers of Ramanujan’s theta function

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