Prime analogues of the Erdős–Kac theorem for elliptic curves
| dc.contributor.author | Liu, Yu-Ru | |
| dc.date.accessioned | 2023-10-03T14:53:32Z | |
| dc.date.available | 2023-10-03T14:53:32Z | |
| dc.date.issued | 2006-08 | |
| dc.description | This article is made available through Elsevier's open archive. This article is available here: https://doi.org/10.1016/j.jnt.2005.10.014 © 2006 Elsevier Inc. All rights reserved. | en |
| dc.description.abstract | Let E/Q be an elliptic curve. For a prime p of good reduction, let E(Fp) be the set of rational points defined over the finite field Fp. We denote by ω(#E(Fp)), the number of distinct prime divisors of #E(Fp). We prove that the quantity (assuming the GRH if E is non-CM) ω(#E(Fp)) − log logp √log logp distributes normally. This result can be viewed as a “prime analogue” of the Erdos–Kac theorem. We also study the normal distribution of the number of distinct prime factors of the exponent of E(Fp). | en |
| dc.description.sponsorship | Research partially supported by an NSERC Discovery Grant. | en |
| dc.identifier.uri | https://doi.org/10.1016/j.jnt.2005.10.014 | |
| dc.identifier.uri | http://hdl.handle.net/10012/19985 | |
| dc.language.iso | en | en |
| dc.publisher | Elseiver | en |
| dc.relation.ispartofseries | Journal of Number Theory;119(2) | |
| dc.subject | prime divisors | en |
| dc.subject | rational points | en |
| dc.subject | elliptic curves | en |
| dc.title | Prime analogues of the Erdős–Kac theorem for elliptic curves | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Liu, Y.-R. (2006). Prime analogues of the erdős–kac theorem for elliptic curves. Journal of Number Theory, 119(2), 155–170. https://doi.org/10.1016/j.jnt.2005.10.014 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Pure Mathematics | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |