Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)

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Moments and non-vanishing of central values of quadratic Hecke L-functions in the Gaussian field

Authors
Peng Gao1, *
1School of Mathematical Sciences, Beihang University, Beijing, P. R. China
*Corresponding author. Email: penggao@buaa.edu.cn
Corresponding Author
Peng Gao
Available Online 2 August 2024.
DOI
10.2991/978-94-6463-463-1_11How to use a DOI?
Keywords
central values; Hecke L-functions; mean values; quadratic Hecke characters
Abstract

We evaluate the first three moments of central values of a family of quadratic Hecke L-functions in the Gaussian field with power saving error terms. In particular, we obtain asymptotic formulas for the first two moments with error terms of size O(X1/2+ε). We also study the first and second mollified moments of the same family of L-functions to show that at least 87.5% of the members of this family have non-vanishing central values.

Copyright
© 2024 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)
Series
Advances in Physics Research
Publication Date
2 August 2024
ISBN
978-94-6463-463-1
ISSN
2352-541X
DOI
10.2991/978-94-6463-463-1_11How to use a DOI?
Copyright
© 2024 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Peng Gao
PY  - 2024
DA  - 2024/08/02
TI  - Moments and non-vanishing of central values of quadratic Hecke L-functions in the Gaussian field
BT  - Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)
PB  - Atlantis Press
SP  - 148
EP  - 183
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-463-1_11
DO  - 10.2991/978-94-6463-463-1_11
ID  - Gao2024
ER  -