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CONVOLUTION SUM ∑k<N/3σ1(3mk)σ1(2n(N-3k))
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  • Journal title : Honam Mathematical Journal
  • Volume 34, Issue 4,  2012, pp.519-531
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2012.34.4.519
 Title & Authors
CONVOLUTION SUM ∑k<N/3σ1(3mk)σ1(2n(N-3k))
Kim, Aeran; Kim, Daeyeoul; Seo, Gyeong-Sig;
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 Abstract
Let . Next, the convolution sums , , etc., are evaluated for all with , .
 Keywords
Divisor functions;Convolution sums;
 Language
English
 Cited by
1.
Bernoulli numbers, convolution sums and congruences of coefficients for certain generating functions, Journal of Inequalities and Applications, 2013, 2013, 1, 225  crossref(new windwow)
 References
1.
PS. Alaca and K. S. Williams, Evaluation of the convolution sums ${\sum}_{l+6m=n}\sigma(l)\sigma(m)$ and ${\sum}_{2l+3m=n}\sigma(l)\sigma(m)$, J. Number Theory, 124 (2007), 491-510. crossref(new window)

2.
PA. Alaca, S. Alaca and K. S. Williams, Evaluation of the convolution sums ${\sum}_{l+18m=n}\sigma(l)\sigma(m)$ and ${\sum}_{2l+9m=n}\sigma(l)\sigma(m)$, Int. J. Math. Sci. 2 (2007), 45-68.

3.
J. G. Huard, Z. M. Ou, B. K. Spearman, and K. S. Williams, Elementary Evaluation of Certain Convolution Sums Involving Divisor Functions, Number theory for the millennium, II, (2002), 229-274.

4.
D. Kim, A. Kim, and A. Sankaranarayanan, Some properties of products of convolution sums, Submitted.