On the Mean Square Value Formula of Dirichlet L-Functions

Abstract:

      In this paper we improve the asymptotic formula obtained by Zhang Wenpeng about the mean square value of Dirichlet L-functions:(?)│L(1/2+it,x)│² by using the method of exponential pairs for the trigonometric sum. We proved the following Theorem:Theorem For any mod q and real t ≥ 3 we have(?) Where r is Euler's constant.