3RD POWER MOMENTS OF THE ERROR TERMS CORRESPONDING TO CERTAIN ARITHMETIC FUNCTIONS

For positive integers n, let d(l(1),M(1);l(2)M(2);n) denote the number of factorizations n=n(1)n(2) where each of the factors n(i) is an ele ment of(I)N belongs to a prescribed congruence class l(i) module M(i) (i=1,2). In this article an asymptotic result is derived for the third power moment of the error term in the formula for the Dirichlet summa tory function of d(l(1),M(1);l(2),M(2);n). This extends a recent resul t of [17] for the classic ''unrestricted'' case of d(n)=d(1,1;1,1;n). Moreover, the technique developed is applied to the analogous problem related to Fourier coefficients of cusp forms.