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.
 

The Normal Distribution of ω(φ(m)) in Function Fields

Thumbnail Image

Files

thesis8.pdf (358.72 KB)

Date

2008-01-28T20:39:15Z

Authors

Li, Li

Journal Title

Journal ISSN

Volume Title

Publisher

University of Waterloo

Abstract

Let ω(m) be the number of distinct prime factors of m. A celebrated theorem of Erdös-Kac states that the quantity (ω(m)-loglog m)/√(loglog m) distributes normally. Let φ(m) be Euler's φ-function. Erdös and Pomerance proved that the quantity(ω(φ(m)-(1/2)(loglog m)^2)\((1/√(3)(loglog m)^(3/2)) also distributes normally. In this thesis, we prove these two results. We also prove a function field analogue of the Erdös-Pomerance Theorem in the setting of the Carlitz module.

Description

Keywords

Number Theory

LC Keywords

Citation

URI

http://hdl.handle.net/10012/3567

Collections

Theses
Pure Mathematics