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2021 Random multiplicative functions: the Selberg-Delange class
Marco Aymone
Author Affiliations +
Electron. Commun. Probab. 26: 1-8 (2021). DOI: 10.1214/21-ECP396

Abstract

Let 12β<1, p be a generic prime number and fβ be a random multiplicative function supported on the squarefree integers such that (fβ(p))p is an i.i.d. sequence of random variables with distribution P(f(p)=1)=β=1P(f(p)=+1). Let Fβ be the Dirichlet series of fβ. We prove a formula involving measure-preserving transformations that relates the Riemann ζ function with the Dirichlet series of Fβ, for certain values of β, and give an application. Further, we prove that the Riemann hypothesis is connected with the mean behavior of a certain weighted partial sum of fβ.

Acknowledgments

I would like to thank the anonymous referee for a careful reading of the paper and for useful suggestions and corrections. The content of this paper is part of the author’s Phd Thesis. I would like to thank my Phd supervisor, Prof. Vladas Sidoravicius, for his encouragement, great intuition, ideas and enthusiasm that played a fundamental role in my academic trajectory.

Citation

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Marco Aymone. "Random multiplicative functions: the Selberg-Delange class." Electron. Commun. Probab. 26 1 - 8, 2021. https://doi.org/10.1214/21-ECP396

Information

Received: 16 February 2021; Accepted: 25 April 2021; Published: 2021
First available in Project Euclid: 5 May 2021

Digital Object Identifier: 10.1214/21-ECP396

Subjects:
Primary: 60F15
Secondary: 11N37

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