Bulletin of the
Korean Mathematical Society
BKMS

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

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Bull. Korean Math. Soc. 2024; 61(1): 65-81

Online first article January 17, 2024      Printed January 31, 2024

https://doi.org/10.4134/BKMS.b230019

Copyright © The Korean Mathematical Society.

Complex moments and the distribution of values of $L(1, \chi_{u})$ in even characteristic

Sunghan Bae, Hwanyup Jung

KAIST; Chungbuk National University

Abstract

In this paper, we announce that the strategy of comparing the complex moments of $L(1,\chi_{u})$ to that of a random Euler product $L(1, {\mb X})$ is also valid in even characteristic case. We give an asymptotic formulas for the complex moments of $L(1,\chi_{u})$ in a large uniform range. We also give $\Omega$-results for the extreme values of $L(1,\chi_{u})$.

Keywords: Complex moments, random Euler product, even characteristic

MSC numbers: 11G20, 11R29, 11R18

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