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A PRODUCT FORMULA FOR COMBINATORIC CONVOLUTION SUMS OF ODD DIVISOR FUNCTIONS

  • Lee, Kwangchul (Department of Mathematics, Chonbuk National University) ;
  • Kim, Daeyeoul (National Institute for Mathematical Sciences) ;
  • Seo, Gyeong-Sig (Department of Mathematics, Institute of Pure and Applied Mathematics, Chonbuk National University)
  • Received : 2015.04.18
  • Accepted : 2016.02.29
  • Published : 2016.06.25

Abstract

If we let $L(2K;n):=\sum_{s=0}^{k-1}(^{2k}_{2s+1})\sum_{m=1}^{n-1}{\sigma}_{2k-2s-1,1}(m;2){\sigma}_{2s+1,1}(n-m;2)$ with $${\sigma}_{k,l}(n;2):=\sum\limits_{{d{\mid}n}\atop{d{\equiv}l(mod2)}}d^k$$, then we get the formula of L(2u; p)L(2v; p)L(2w; p).

Keywords

Divisor functions;Convolution sums;Bernoulli polynomials

References

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