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 ∈ [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.