We use the recent evaluation of certain convolution sums involving the sum of divisors function to determine the number of representations of a positive integer by certain diagonal octonary quadratic forms whose coefficients are 1, 2 or 4.

Convolution sums, Divisor functions, Octonary quadratic forms
dx.doi.org/10.1142/S179304211000279X
International Journal of Number Theory
School of Mathematics and Statistics

Alaca, A, Alaca, S, & Williams, K.S. (2010). Fourteen octonary quadratic forms. International Journal of Number Theory, 6(1), 37–50. doi:10.1142/S179304211000279X