Sofos, E. (2023) Gaps between prime divisors and analogues in Diophantine geometry. Glasgow Mathematical Journal, 65(S1), S129-S147. (doi: 10.1017/S0017089522000398)
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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 Qp -point on a random variety are Poisson distributed.
| Item Type: | Articles |
|---|---|
| Additional Information: | While working on this paper, the author was supported by EPSRC New Horizons grant EP/V048236/1. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Sofos, Dr Efthymios |
| Authors: | Sofos, E. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Glasgow Mathematical Journal |
| Publisher: | Cambridge University Press |
| ISSN: | 0017-0895 |
| ISSN (Online): | 1469-509X |
| Published Online: | 27 February 2023 |
| Copyright Holders: | Copyright © 2023 The Authors |
| First Published: | First published in Glasgow Mathematical Journal 65(S1): S129-S147 |
| Publisher Policy: | Reproduced under a Creative Commons License |
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