On asymptotic properties of the generalized Dirichlet L-functions.

Let q ≥ 3 be an integer, χ denote a Dirichlet character modulo q , for any real number a ≥ 0 , we define the generalized Dirichlet L -functions L (s , χ , a) = ∑ n = 1 ∞ χ (n) (n + a) s , where s = σ + i t with σ > 1 and t both real. It can be extended to all s by analytic continuation. In this paper, we study the mean value properties of the generalized Dirichlet L -functions, and obtain several sharp asymptotic formulae by using analytic method. [ABSTRACT FROM AUTHOR]