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Bull. Korean Math. Soc. 2022; 59(2): 431-452

Online first article March 31, 2022      Printed March 31, 2022

https://doi.org/10.4134/BKMS.b210330

Copyright © The Korean Mathematical Society.

Mean values of derivatives of $L$-functions in even characteristic

Sunghan Bae, Hwanyup Jung

KAIST; Chungbuk National University

Abstract

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For any positive integer $\mu$, we compute the mean value of the $\mu$-th derivative of quadratic Dirichlet $L$-functions over the rational function field $\mathbb{F}_{q}(t)$, where $q$ is a power of $2$.

Keywords: Function fields, even characteristic, derivatives of $L$-functions, moments of $L$-functions, quadratic Dirichlet $L$-functions

MSC numbers: 11M38, 11M06, 11G20, 11M50

Supported by: The second author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (2020R1F1A1A01066105).

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