Geodesic
Gaps between prime divisors and analogues in Diophantine geometry
Glasgow mathematical journal, Tome 65 (2023), pp. S129-S147

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DOI

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 $\mathbb{Q}_p$-point on a random variety are Poisson distributed.
DOI : 10.1017/S0017089522000398
Mots-clés : prime divisors, local solubility 
Sofos, Efthymios. Gaps between prime divisors and analogues in Diophantine geometry. Glasgow mathematical journal, Tome 65 (2023), pp. S129-S147. doi: 10.1017/S0017089522000398
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