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Evaluation of the convolution sums σa1m1+a2m2+a3m3+a4m4=nσ (m1) σ (m2) σ (m3) σ (m4) with lcm (α1,a2,a3,a4) ≤ 4

Title
Evaluation of the convolution sums σa1m1+a2m2+a3m3+a4m4=nσ (m1) σ (m2) σ (m3) σ (m4) with lcm (α1,a2,a3,a4) ≤ 4
Authors
Lee J.Park Y.K.
Ewha Authors
박윤경
SCOPUS Author ID
박윤경scopus
Issue Date
2017
Journal Title
International Journal of Number Theory
ISSN
1793-0421JCR Link
Citation
vol. 13, no. 8, pp. 2155 - 2173
Keywords
Convolution sumquasimodular formsums of divisor functionsthe number of representation by quadratic forms
Publisher
World Scientific Publishing Co. Pte Ltd
Indexed
SCIE; SCOPUS WOS scopus
Abstract
The generating functions of divisor functions are quasimodular forms of weight 2 and the product of them is a quasimodular form of higher weight. In this work, we evaluate the convolution sumsa1m1+a2m2+a3m3+a4m4=nσ(m1)σ(m2)σ(m3)σ(m4) for the positive integers a1,a2,a3,a4, and n with lcm(a1,a2,a3,a4) ≤ 4. We reprove the known formulas for the number of representations of a positive integer n by each of the quadratic forms j=016x j2 and j=18(x 2j-12 + x 2j-1x2j + x2j2) as an application of the new identities proved in this paper. © 2017 World Scientific Publishing Company.
DOI
10.1142/S1793042117501160
Appears in Collections:
연구기관 > 수리과학연구소 > Journal papers
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