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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
- 박윤경
- Issue Date
- 2017
- Journal Title
- International Journal of Number Theory
- ISSN
- 1793-0421
- Citation
- International Journal of Number Theory vol. 13, no. 8, pp. 2155 - 2173
- Keywords
- Convolution sum; quasimodular form; sums of divisor functions; the number of representation by quadratic forms
- Publisher
- World Scientific Publishing Co. Pte Ltd
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- 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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