Abstract
In this paper, the convolution sums Sigma(i+12j)=n(sigma(l)sigma 3(m)), Sigma(3i+4j)= n(sigma(l) sigma 3(m)), Sigma(4i+3j)=n(sigma(l)sigma 3(m)) and Sigma(12i+j)=n(sigma(l)sigma 3(m)) are evaluated for all n (sic) N, and their evaluations are used to determine the number of representation of a positive integer n by the forms x(1)(2) + x(2)(2) + x(3)(2) + x(4)(2) + x(5)(2) + x(6)(2) + x(7)(2) + x(8)(2) + 3x(9)(2) + 3x(10)(2) + 3x(11)(2) + 3x(12)(2) and x(1)(2) + x(2)(2) + x(3)(2) + x(4)(2) + 3x(5)(2) + 3x(6)(2) + 3x(7)(2) + 3x(8)(2) + 3x(9)(2) + 3x(10)(2) + 3x(11)(2) + 3x(12)(2).