Let , p be a generic prime number and be a random multiplicative function supported on the squarefree integers such that is an i.i.d. sequence of random variables with distribution . Let be the Dirichlet series of . We prove a formula involving measure-preserving transformations that relates the Riemann ζ function with the Dirichlet series of , 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 .
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.
"Random multiplicative functions: the Selberg-Delange class." Electron. Commun. Probab. 26 1 - 8, 2021. https://doi.org/10.1214/21-ECP396