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
Jungyun Lee. Yoonjin Lee. "Mean Values of Derivatives of $L$-functions for Cyclotomic Characters in Function Fields." Taiwanese J. Math. 26 (6) 1113 - 1131, December, 2022. https://doi.org/10.11650/tjm/220701
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