Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CONVOLUTION SUMS ARISING FROM DIVISOR FUNCTIONS

  • Kim, Aeran (Department of Mathematics and Institute of Pure and Applied Mathematics Chonbuk National University) ;
  • Kim, Daeyeoul (National Institute for Mathematical Sciences) ;
  • Yan, Li (Department of Applied Mathematics China Agriculture University)
  • Received : 2012.03.26
  • Published : 2013.03.01
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Abstract

Let ${\sigma}_s(N)$ denote the sum of the sth powers of the positive divisors of a positive integer N and let $\tilde{\sigma}_s(N)={\sum}_{d|N}(-1)^{d-1}d^s$ with $d$, N, and s positive integers. Hahn [12] proved that $$16\sum_{k. In this paper, we give a generalization of Hahn's result. Furthermore, we find the formula ${\sum}_{k=1}^{N-1}\tilde{\sigma}_1(2^{n-m}k)\tilde{\sigma}_3(2^nN-2^nk)$ for $m(0{\leq}m{\leq}n)$.

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References

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