Theta-function identities and the explicit formulas for theta-function and their applications
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Publication:1827128
DOI10.1016/j.jmaa.2003.12.009zbMath1060.11027OpenAlexW1966874439WikidataQ56270731 ScholiaQ56270731MaRDI QIDQ1827128
Publication date: 6 August 2004
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.2003.12.009
Theta series; Weil representation; theta correspondences (11F27) Dedekind eta function, Dedekind sums (11F20) Elliptic functions and integrals (33E05)
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Cites Work
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- Modular equations for the Rogers-Ramanujan continued fraction and the Dedekind eta-function
- Evaluations of the Rogers–Ramanujan continued fraction R(q) by modular equations
- The evaluation in terms of Γ-functions of the periods of elliptic curves admitting complex multiplication
- On Epstein's Zeta-function.
- A Closed Form Evaluation of the Elliptic Integral