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- Title
Linear Statistics of Low‐Lying Zeros of L‐Functions.
- Authors
HUGHES, C. P.; RUDNICK, Z.
- Abstract
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.
- Subjects
LINEAR algebra; L-functions; DIRICHLET forms; GAUSSIAN processes; RANDOM matrices
- Publication
Quarterly Journal of Mathematics, 2003, Vol 54, Issue 3, p309
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hag021