EVALUATION OF THE CONVOLUTION SUMS ∑i+3j=nσ(i)σ3(j) AND ∑3i+j=nσ(i)σ3(j)

DOI10.1142/S1793042113500838zbMath1310.11008OpenAlexW1833956638MaRDI QIDQ5746419

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

Publication date: 18 February 2014

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

Full work available at URL: https://doi.org/10.1142/s1793042113500838

zbMATH Keywords

Eisenstein seriesconvolution sumssum of divisors function

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (7)

Evaluation of the convolution sums \(\sum_{ak+bl+cm}=\sigma(k)\sigma(l)\sigma(m)\) with \(\text{lcm}(a,b,c) \leq 6\) ⋮ On the number of representations of certain quadratic forms and a formula for the Ramanujan tau function ⋮ On the number of representations of an integer by certain quadratic forms in sixteen variables ⋮ A simple extension of Ramanujan-Serre derivative map and some applications ⋮ Evaluation of some convolution sums and representation of integers by certain quadratic forms in 12 variables ⋮ On the number of representations of certain quadratic forms in 20 and 24 variables ⋮ Representation numbers of certain quaternary quadratic forms in a genus consisting of a single class

Cites Work

• On the two-dimensional theta functions of the Borweins

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