The convolution sum ∑m<n/8 σ(m) σ(n-8m) is evaluated for all n ε ℕ. This evaluation is used to determine the number of representations of n by the quadratic form x2 1 + x2 2 + x2 3 + x2 4 +2x2 5 +2x2 6 +2x2 7 +2x2 8.

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Keywords Convolution sums, Divisor functions, Eisenstein series
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Journal Pacific Journal of Mathematics
Williams, K.S. (2006). The convolution sum ∑mPacific Journal of Mathematics, 228(2), 387–396. doi:10.2140/pjm.2006.228.387