A penalised model reproducing the mod-Poisson fluctuations in the Sathe-Selberg theorem
Probability
2017-01-13 v1
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 Sathe-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
Cite
@article{arxiv.1701.03432,
title = {A penalised model reproducing the mod-Poisson fluctuations in the Sathe-Selberg theorem},
author = {Yacine Barhoumi-Andréani},
journal= {arXiv preprint arXiv:1701.03432},
year = {2017}
}