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arXiv · 2106.00298

Gaps between prime divisors and analogues in Diophantine geometry

E. Sofos
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Abstract

Erd\H{o}s 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 $\mathbb{Q}_p$-point on a random variety are Poisson distributed.

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E. Sofos. 2021-06-01. Gaps between prime divisors and analogues in Diophantine geometry. https://arxiv.org/abs/2106.00298

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