THE NUMBER OF REPRESENTATIONS OF AN INTEGER AS A SUM INVOLVING GENERALIZED PENTAGONAL NUMBERS

DOI10.1142/S1793042112500613zbMath1247.11050OpenAlexW2068972047MaRDI QIDQ2890254

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

Publication date: 8 June 2012

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

Full work available at URL: https://doi.org/10.1142/s1793042112500613

zbMATH Keywords

theta functionsgeneralized pentagonal numbers

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Theta series; Weil representation; theta correspondences (11F27)

Cites Work

• Evaluation of the convolution sums \(\sum _{l+6m=n}\sigma (l)\sigma (m)\) and \(\sum _{2l+3m=n}\sigma (l)\sigma (m)\)
• Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions
• On the two-dimensional theta functions of the Borweins
• THETA FUNCTION IDENTITIES AND REPRESENTATIONS BY CERTAIN QUATERNARY QUADRATIC FORMS
• NOTE ON SOME PARTITION FORMULAE

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