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Twisted second moments of Dirichlet L-functions with applications to weighted one-level density
Abstract
We give an asymptotic formula for the twisted second moment of a fixed Dirichlet L-function in the t-aspect. This is a generalization of Selberg's asymptotic formula for the twisted second moment of the Riemann zeta function. As an application, we observe the change and the stability of the weighted one-level density of zeros of a fixed Dirichlet L-function.
Related
- Improved first moments of primitive quartic and sextic Dirichlet L-functions
- Finite Cotangent Power Sums Weighted by Additive Characters With Application to Mean Values of Additive-and-Multiplicatively Twisted L-Functions
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BibTeX
@misc{inumaru2026twisted,
title = {{Twisted second moments of Dirichlet $L$-functions with applications to weighted one-level density}},
author = {Naoto Inumaru and Shingo Sugiyama},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41394},
eprint = {2610.41394},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41394},
}
RIS
TY - UNPB
TI - Twisted second moments of Dirichlet L-functions with applications to weighted one-level density
AU - Naoto Inumaru
AU - Shingo Sugiyama
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41394
UR - https://arxiv.org/abs/2610.41394
AB - We give an asymptotic formula for the twisted second moment of a fixed Dirichlet L-function in the t-aspect. This is a generalization of Selberg's asymptotic formula for the twisted second moment of the Riemann zeta function. As an application, we observe the change and the stability of the weighted one-level density of zeros of a fixed Dirichlet L-function.
ER -