$n$-level density of the low-lying zeros of quadratic Dirichlet $L$-functions

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dc.creatorGao, Peng
dc.date2008-06-30
dc.date.accessioned2026-07-07T09:47:26Z
dc.date.available2026-07-07T09:47:26Z
dc.descriptionThe Density Conjecture of Katz and Sarnak associates a classical compact group to each reasonable family of $L$-functions. Under the assumption of the Generalized Riemann Hypothesis, Rubinstein computed the $n$-level density of low-lying zeros for the family of quadratic Dirichlet $L$-functions in the case that the Fourier transform $\hat{f}(u)$ of any test function $f$ is supported in the region $\sum^n_{j=1}u_j < 1$ and showed that the result agrees with the Density Conjecture. In this paper, we improve Rubinstein's result on computing the $n$-level density for the Fourier transform $\hat{f}(u)$ being supported in the region $\sum^n_{j=1}u_j < 2$.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/0806.4830
dc.identifierhttp://arxiv.org/abs/0806.4830
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163874
dc.subjectNumber Theory
dc.subject11M26
dc.title$n$-level density of the low-lying zeros of quadratic Dirichlet $L$-functions
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