On higher-power moments of the error term for the divisor problem with congruence conditions

For a positive integer n, the divisor function with congruence conditions d(n; l ₁, M ₁, l ₂, M ₂) denotes the number of factorizations n?=?n ₁ n ₂, where each of the factors ${n_iinmathbb{N}}$ belongs to a prescribed congruence class l _i modulo M _i ? (i?=?1, 2). In this paper we study the higher power moments of the error term in the asymptotic formula of ${sumnolimits_{nleq M_1M_2x}d(n;l_1,M_1,l_2,M_2)}$ .