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2022 Mean Values of Derivatives of $L$-functions for Cyclotomic Characters in Function Fields
Jungyun Lee, Yoonjin Lee
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Taiwanese J. Math. Advance Publication 1-19 (2022). DOI: 10.11650/tjm/220701

Abstract

We compute the mean value of derivatives of $L$-functions for cyclotomic characters in function fields. We also show the non-vanishing property of derivatives of $L$-functions for cyclotomic characters in function fields.

Funding Statement

J. Lee is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1I1A3057692). Y. Lee is a corresponding author and supported by the Ewha Womans University Research Grant of 2021, the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2022R1A2C1003203), and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1A6A1A11051177).

Acknowledgments

The authors would like to thank the reviewers for very helpful comments.

Citation

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Jungyun Lee. Yoonjin Lee. "Mean Values of Derivatives of $L$-functions for Cyclotomic Characters in Function Fields." Taiwanese J. Math. Advance Publication 1 - 19, 2022. https://doi.org/10.11650/tjm/220701

Information

Published: 2022
First available in Project Euclid: 12 July 2022

Digital Object Identifier: 10.11650/tjm/220701

Subjects:
Primary: 11R29 , 11R58

Keywords: $L$-function , central value , function field , mean value

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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