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

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

2002-08-29

arxiv.org/abs/math/0208230v2

Mathematics

Number Theory

Replacement has some minor changes and the references have been updated

Scientific paper

We 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.

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