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

摘要

We study the mean values of the first and the second derivative of quadratic Dirichlet L-functions L(s, chi(D)) over the rational function field. We show that the moments of first derivatives L'(1/2, chi(D)) are just constant multiples of the moments of L(1/2, chi(D)). For the second derivatives, we improve the error term by q(1/2(1+epsilon)) and show that there is an extra term of size g(3)q(2n+1/3) in the asymptotic formula of Andrade and Rajagopal for the first moment of L ''(1/2,chi(D)). (C) 2019 Elsevier Inc. All rights reserved.