An elementary proof of Ramanujan's circular summation formula and its generalizations
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Publication:427275
DOI10.1007/s11139-011-9364-4zbMath1282.11040OpenAlexW2035431994MaRDI QIDQ427275
Publication date: 13 June 2012
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11139-011-9364-4
Theta series; Weil representation; theta correspondences (11F27) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) 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 ⋮ 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
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- A generalized circular summation of theta function and its application
- On the circular summation of the eleventh powers of Ramanujan's theta function
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- Circular summation of the 13th powers of Ramanujan's theta function
- Circular summations of theta functions in Ramanujan's lost notebook
- The root lattice $A^*_n$ and Ramanujan’s circular summation of theta functions
- Additive decompositions of θ-functions of multiple arguments
- Some Cubic Modular Identities of Ramanujan
- The sixth, eighth, ninth, and tenth powers of Ramanujan’s theta function
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