UWSpace is currently experiencing technical difficulties resulting from its recent migration to a new version of its software. These technical issues are not affecting the submission and browse features of the site. UWaterloo community members may continue submitting items to UWSpace. We apologize for the inconvenience, and are actively working to resolve these technical issues.
 

Prime analogues of the Erdős–Kac theorem for elliptic curves

Thumbnail Image

Files

24-published.pdf (146.23 KB)

Date

2006-08

Authors

Liu, Yu-Ru

Journal Title

Journal ISSN

Volume Title

Publisher

Elseiver

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).

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.

Keywords

prime divisors, rational points, elliptic curves

LC Keywords

Citation

URI

https://doi.org/10.1016/j.jnt.2005.10.014
 http://hdl.handle.net/10012/19985

Collections

Waterloo Research