关于L-函数的一类渐近公式(Ⅰ)

On a Class Asymptotic Formula of L-functions

对整数 q>3,设 x 表示模 q 的 Dirichlct 特征,L(s,x)是对应于 x 的 L-函数,对给定的0<σ<1及任意实数 t,设 s=σ+it。

The main purpose of this paper is to give a sharper asymptotic formula for the mean value sum from to xmodq~*L(σ+it,x)L(1-σ-it,(?)).Where the summation is over all primitive Dirichlet's charactcrs x(modq).This will be derived from the analytic method and the estimate of character sums.