A hybird mean value involving gauss sums and character sums

Abstract

Let χ be a Dirichlet character modulo q > 2, and L(s, χ) denotes the Dirichlet L-function corresponding to χ. The main purpose of this paper is using the estimate for character sums and the analytic method to study the mean value properties of \( \frac{{L'}} {L}(1,\chi ) \) with the weight of Gauss sums and character sums, and give an interesting mean value formula for it.