Gaps between prime divisors and analogues in Diophantine geometry

2021/06/01 by Efthymios Sofos, Sofos, E. · 1 citation
Mathematics · #11K65 #14G05 #60F05 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2106.00298

openalex publication_date 2021/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Erdős considered the second moment of the gap-counting function of prime divisors in 1946 and proved an upper bound that is not of the right order of magnitude. We prove asymptotics for all moments. Furthermore, we prove a generalisation stating that the gaps between primes p for which there is no ℚ_p-point on a random variety are Poisson distributed.

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