Eisenstein series identities involving the Borweins' cubic theta functions

DOI10.1155/2012/181264zbMath1278.11049DBLPjournals/jam/XiaY12OpenAlexW2003347634WikidataQ58905834 ScholiaQ58905834MaRDI QIDQ1760582

Ernest X. W. Xia, Olivia X. M. Yao

Publication date: 15 November 2012

Published in: Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2012/181264

Mathematics Subject Classification ID

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

Related Items (3)

Some new Eisenstein series containing the Borweins' cubic theta functions and convolution sum \(\sum_{i+4j=n} \sigma (i)\sigma (j)\) ⋮ Relation between Borweins' cubic theta functions and Ramanujan's Eisenstein series ⋮ On some Eisenstein series identities associated with Borwein's cubic theta functions

Cites Work

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• Evaluation of the convolution sums \(\sum _{l+6m=n}\sigma (l)\sigma (m)\) and \(\sum _{2l+3m=n}\sigma (l)\sigma (m)\)
• The convolution sum \(\sum_{m<n/8} \sigma(m) \sigma(n-8m)\)
• The Borwein's cubic theta function identity and some cubic modular identities of Ramanujan
• On the two-dimensional theta functions of the Borweins
• EVALUATING CONVOLUTION SUMS OF THE DIVISOR FUNCTION BY QUASIMODULAR FORMS
• Evaluation of the convolution sums \sum_{l+18m=n} \sigma(l) \sigma(m) and \sum_{2l+9m=n} \sigma(l) \sigma(m)
• On Ramanujan's cubic transformation formula for 2 F 1(1/3, 2/3; 1; z)
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• A Cubic Counterpart of Jacobi's Identity and the AGM
• The Convolution Sum Σ_m<n/16σ(m)σ(n – 16m)
• Evaluation of two convolution sums involving the sum of divisors function
• THE CONVOLUTION SUM $\sum\limits_{m<n/9}\sigma(m)\sigma(n-9m)$
• Some Eisenstein series identities

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