On the mean square of an arithmetical error term of the Selberg class in short intervals

Abstract

Let [Formula: see text] be a Dirichlet series in the Selberg class of degree [Formula: see text] and let [Formula: see text] be the arithmetical error term of [Formula: see text]. We derive two kinds of the mean square estimates of [Formula: see text] in short intervals of Jutila’s type. Our method is based on the truncated Tong-type formula of [Formula: see text]. We also give several applications of these estimates in the arithmetical problems.