On a problem analogues to Lehmer’s and Hurwitz zeta-function

The main purpose of this paper is to introduce a problem analogous to Lehmer’s and study a mean value of its error part with the weight of Hurwitz zeta-function by using the properties of character sums and the analytic method. A sharp asymptotic formula was given and a connection between the problem analogous to Lehmer’s and Hurwitz zeta-function was established.