The convolution sum ∑m<n/16σ(m)σ(n - 16m) is evaluated for all n ∈ ℕ. This evaluation is used to determine the number of representations of n by the quadratic form x1 2 + x2 2 + x3 2 + x4 2 + 4x5 2 + 4x6 2 + 4x 7 2 + 4x8 2.

Additional Metadata
Keywords Convolution sums, Divisor functions, Eisenstein series
Journal Canadian Mathematical Bulletin
Citation
Alaca, A, Alaca, S, & Williams, K.S. (2008). The convolution sum ∑mCanadian Mathematical Bulletin, 51(1), 3–14.