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arXiv · 2511.14234

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

Michael Cranston·Mariia Khodiakova
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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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Michael Cranston, Mariia Khodiakova. 2025-11-18. Large deviations for number of irreducible divisors of the Dirichlet series distribution. https://arxiv.org/abs/2511.14234

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