Note on the mean values of derivatives of quadratic Dirichlet L-functions in function fields

Abstract

We study the mean values of the first and the second derivative of quadratic Dirichlet L-functions L(s,χD) over the rational function field. We show that the moments of first derivatives L′(12,χD) are just constant multiples of the moments of L(12,χD). For the second derivatives, we improve the error term by q12(1+ϵ) and show that there is an extra term of size g3q2g+13 in the asymptotic formula of Andrade and Rajagopal for the first moment of L″(12,χD).