Mesoscopic fluctuations of the zeta zeros

Research output: Contribution to journalArticle

Abstract

We prove a multidimensional extension of Selberg's central limit theorem for log ζ, in which non-trivial correlations appear. In particular, this answers a question by Coram and Diaconis about the mesoscopic fluctuations of the zeros of the Riemann zeta function. Similar results are given in the context of random matrices from the unitary group. This shows the correspondence n ↔ log t not only between the dimension of the matrix and the height on the critical line, but also, in a local scale, for small deviations from the critical axis or the unit circle.

Original languageEnglish (US)
Pages (from-to)479-500
Number of pages22
JournalProbability Theory and Related Fields
Volume148
Issue number3-4
DOIs
StatePublished - Nov 2010

Keywords

  • Central limit theorem
  • Zeta and L-functions

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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