# Bulletin of theKorean Mathematical SocietyBKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

## Article

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

Published online March 31, 2022 https://doi.org/10.4134/BKMS.b210330

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

Sunghan Bae, Hwanyup Jung

KAIST; Chungbuk National University

### Abstract

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