Journal of Advances in Mathematics and Computer Science

The Convolution Sum ∑m<n/8 σ3(m)σ3(n-8m)

Aeran Kim *

Department of Mathematics, Chonbuk National University, Chonju, Chonbuk 561-756, South Korea.

*Author to whom correspondence should be addressed.

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Abstract

The convolution sum  m<n=8 _3(m)_3(n - 8m) is evaluated for all n 2 N. This evaluation is used to determine the formulae of the convolution sums   etc., and the number of representations of n through the sum of eight triangular numbers. 

Keywords: Divisor functions : Convolution sum.

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