The Normal Distribution of ω(φ(m)) in Function Fields
| dc.contributor.author | Li, Li | |
| dc.date.accessioned | 2008-01-28T20:39:15Z | |
| dc.date.available | 2008-01-28T20:39:15Z | |
| dc.date.issued | 2008-01-28T20:39:15Z | |
| dc.date.submitted | 2007 | |
| dc.description.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. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/3567 | |
| dc.language.iso | en | en |
| dc.pending | false | en |
| dc.publisher | University of Waterloo | en |
| dc.subject | Number Theory | en |
| dc.subject.program | Pure Mathematics | en |
| dc.title | The Normal Distribution of ω(φ(m)) in Function Fields | en |
| dc.type | Master Thesis | en |
| uws-etd.degree | Master of Mathematics | en |
| uws-etd.degree.department | Pure Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |