A Penalised Model Reproducing the Mod-Poisson Fluctuations in the Sathé–Selberg Theorem

Yacine Barhoumi-Andréani ()
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Yacine Barhoumi-Andréani: Ruhr-Universität Bochum

Journal of Theoretical Probability, 2020, vol. 33, issue 2, 567-589

Abstract: Abstract We construct a probabilistic model for the number of divisors of a random uniform integer that converges in the mod-Poisson sense to the same limiting function as its original counterpart, the one arising in the Sathé–Selberg theorem. This construction involves a conditioning and gives an alternative perspective to the usual paradigm of “hybrid product” models developed by Gonek, Hughes and Keating in the case of the Riemann Zeta function.

Keywords: Mod-Poisson convergence; Sathe–Selberg theorem; Primes; Probabilistic models; 60E10; 60E05; 60F05; 60G50; 60F99; 11K99; 11K65 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00961-6

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