Large deviations for number of irreducible divisors of the Dirichlet series distribution

2025/11/18 by Cranston, Michael, Khodiakova, Mariia
#11A41 #11R42 #11R59 #60F10 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2511.14234

Abstract

In this paper we produce precise large deviation estimates through the lens of mod-Poisson convergence. We apply a general result to various examples from number theory, Dedekind domains and polynomials over finite fields when an element is selected using a distribution based on a Dirichlet series.

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