On some sums at the a-points of the k-th derivatives of the Dirichlet L-functions

Abstract

Let L (k) (s, χ) be the k -th derivative of the Dirichlet L-function associated with a primitive character χ mod q and a be a complex number. The solutions of L (k) (s, χ) = a are called a-points. In this paper, we give an asymptotic formula for the sums X ρ (k) 0,χ :0