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

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.

arXiv commentThe support conditions in main theorems are improved. Remark 3.5 is added

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