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December 2021 The mixed second moment of quadratic Dirichlet L-functions over function fields
Goran Djanković, Dragan Ðokić
Rocky Mountain J. Math. 51(6): 2003-2017 (December 2021). DOI: 10.1216/rmj.2021.51.2003

Abstract

We investigate the mixed second moment involving the second derivative at the central point of a family of quadratic Dirichlet L-functions over 𝔽q(t), associated to the hyperelliptic curves of genus g. We compute the full degree five polynomial in the asymptotic expansion of the mixed second moment when the cardinality q of the finite field is fixed and the genus g tends to infinity. This is a partial analogue of classical Ingham’s result about the Riemann zeta function.

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Goran Djanković. Dragan Ðokić. "The mixed second moment of quadratic Dirichlet L-functions over function fields." Rocky Mountain J. Math. 51 (6) 2003 - 2017, December 2021. https://doi.org/10.1216/rmj.2021.51.2003

Information

Received: 29 October 2020; Revised: 25 March 2021; Accepted: 29 March 2021; Published: December 2021
First available in Project Euclid: 22 March 2022

Digital Object Identifier: 10.1216/rmj.2021.51.2003

Subjects:
Primary: 11M38
Secondary: 11G20 , 11M06 , 11M50 , 11R58

Keywords: derivatives of L-functions , moments of L-functions , quadratic Dirichlet L-functions , rational function fields

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 6 • December 2021
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