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 -