Multidimensional Selberg theorem and fluctuations of the zeta zeros via Malliavin calculus

2016/01/11 by Ciprian A. Tudor, Ciprian Tudor, Tudor, Ciprian
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Graph theory and applications #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1601.02515

arxiv created 2016/01/11 · openalex publication_date 2016/01/11 · arxiv updated 2016/01/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We give new contributions on the distribution of the zeros of the Riemann zeta function by using the techniques of the Malliavin calculus. In particular, we obtain the error bound in the multidimensional Selberg' s central limit theorem concerning the zeta zeros on the critical line and we discuss some consequences concerning the asymptotic behavior of the mesoscopic fluctuations of the zeta zeros.

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