On the fourth power moment of the error term for the divisor problem with congruence conditions

Abstract

Let [Formula: see text] denote the number of factorizations [Formula: see text], where each of the factors [Formula: see text] belongs to a prescribed congruence class [Formula: see text]. Let [Formula: see text] be the error term of the asymptotic formula of [Formula: see text]. In this paper, we establish an asymptotic formula of the fourth power moment of [Formula: see text] and prove that [Formula: see text] with [Formula: see text], which improves the previous value [Formula: see text] of Liu [On higher-power moments of the error term for the divisor problem with congruence conditions, Monatsh. Math. 163(2) (2011) 175–195].