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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2013; 50(2): 331-360

Printed March 1, 2013

https://doi.org/10.4134/JKMS.2013.50.2.331

Copyright © The Korean Mathematical Society.

Convolution sums arising from divisor functions

Aeran Kim, Daeyeoul Kim, and Li Yan

Chonbuk National University, National Institute for Mathematical Sciences, China Agriculture University

Abstract

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Let $\sigma_s(N)$ denote the sum of the $s$th powers of the positive divisors of a positive integer $N$ and let $\widetilde{\sigma}_s(N) = \sum_{d|N} (-1)^{d-1}d^s$ with $d$, $N$, and $s$ positive integers. Hahn \cite{Hahn} proved that $$ 16\sum_{k

Keywords: Weierstrass $\wp(x)$ functions, convolution sums

MSC numbers: 11A67

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