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

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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.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2019-05
Language
English
Article Type
Article
Citation

FINITE FIELDS AND THEIR APPLICATIONS, v.57, pp.249 - 267

ISSN
1071-5797
DOI
10.1016/j.ffa.2019.02.010
URI
http://hdl.handle.net/10203/261705
Appears in Collection
MA-Journal Papers(저널논문)
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