TY - JOUR

T1 - Linear statistics of low-lying zeros of L-functions

AU - Hughes, C. P.

AU - Rudnick, Z.

N1 - Funding Information:
Supported in part by the EC TMR network ‘Mathematical aspects of Quantum Chaos’, EC-contract no. HPRN-CT-2000-00103.

PY - 2003/9

Y1 - 2003/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0142026313&partnerID=8YFLogxK

U2 - 10.1093/qmath/hag021

DO - 10.1093/qmath/hag021

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AN - SCOPUS:0142026313

VL - 54

SP - 309

EP - 333

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

SN - 0033-5606

IS - 3

ER -