호남수학학술지 (Honam Mathematical Journal)

  • 제34권4호
  • /
  • Pages.519-531
  • /
  • 2012
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

CONVOLUTION SUM ∑k<N/3σ1(3mk)σ1(2n(N-3k))

  • Kim, Aeran (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University) ;
  • Kim, Daeyeoul (National Institute for Mathematical Sciences) ;
  • Seo, Gyeong-Sig (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University)
  • 투고 : 2012.08.15
  • 심사 : 2012.11.19
  • 발행 : 2012.12.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Let ${\sigma}_s(N)={\sum}_{d{\mid}N}d^s$. Next, the convolution sums ${\sum}_{k<N/3}{\sigma}_1(3^mk){\sigma}_1(2^n(N-3k))$, ${\sum}_{<N/3}{\sigma}_1(2^mk){\sigma}_1(3^n(N-3k))$, etc., are evaluated for all $N{\in}\mathbb{N}$ with $m$, $n{\in}\mathbb{N}{\cup}\{0\}$.

키워드

참고문헌

  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. https://doi.org/10.1016/j.jnt.2006.10.004
  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.

피인용 문헌

  1. Bernoulli numbers, convolution sums and congruences of coefficients for certain generating functions vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-225