# Weighted one-level density of low-lying zeros of Dirichlet $L$-functions

Source: [Weighted one-level density of low-lying zeros of Dirichlet $L$-functions](<https://www.sota2.com/research/paper/68fa59ad1e209131ce9b94e2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T05:24:35.209Z

Authors: Shingo Sugiyama, Ade Irma Suriajaya

Published: 2022-01-02T09:25:29.000Z

## Abstract

In this paper, we compute the one-level density of low-lying zeros of Dirichlet $L$-functions in a family weighted by special values of Dirichlet $L$-functions at a fixed $s \\in \[1/2, 1)$. We verify both Fazzari's conjecture and the first author's conjecture on the weighted one-level density for our family of $L$-functions.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2201.00326>)

[PDF](<https://arxiv.org/pdf/2201.00326.pdf>)