Linear statistics of low-lying zeros of L--functions

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dc.creatorHughes, C. P.
dc.creatorRudnick, Z.
dc.date2002-08-29
dc.date2002-12-04
dc.date.accessioned2026-07-07T04:50:27Z
dc.date.available2026-07-07T04:50:27Z
dc.descriptionWe consider linear statistics of the scaled zeros of Dirichlet $L$--functions, and show that the first few moments converge to the Gaussian moments. The number of Gaussian moments depends on the particular statistic considered. The same phenomenon is found in Random Matrix Theory, where we consider linear statistics of scaled eigenphases for matrices in the unitary group. In that case the higher moments are no longer Gaussian. We conjecture that this also happens for Dirichlet $L$--functions.
dc.descriptionReplacement has some minor changes and the references have been updated
dc.identifierhttps://arxiv.org/abs/math/0208230
dc.identifierhttp://arxiv.org/abs/math/0208230
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64798
dc.subjectNumber Theory
dc.titleLinear statistics of low-lying zeros of L--functions
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