Linear statistics of low-lying zeros of L-functions
By C. Hughes, Z. Rudnick. 2002
120 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f70741f52c1f155e5bdc6a23505a529623d9d737
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- Statistics for low-lying zeros of symmetric power L-functions in the level aspect (2007, background): “Remark 8 This result is another evidence for mock-Gaussian behaviour (see [13, 14, 15] for instance).”