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.

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