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

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

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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))...

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Main Author: Li, Li
Language:en
Published: 2008
Subjects:
Number Theory
Pure Mathematics
Online Access:http://hdl.handle.net/10012/3567
id ndltd-WATERLOO-oai-uwspace.uwaterloo.ca-10012-3567
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spelling ndltd-WATERLOO-oai-uwspace.uwaterloo.ca-10012-35672013-01-08T18:50:59ZLi, Li2008-01-28T20:39:15Z2008-01-28T20:39:15Z2008-01-28T20:39:15Z2007http://hdl.handle.net/10012/3567Let 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.enNumber TheoryThe Normal Distribution of ω(φ(m)) in Function FieldsThesis or DissertationPure MathematicsMaster of MathematicsPure Mathematics
collection NDLTD
language en
sources NDLTD
topic Number Theory
Pure Mathematics
spellingShingle Number Theory
Pure Mathematics
Li, Li
The Normal Distribution of ω(φ(m)) in Function Fields
description 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.
author Li, Li
author_facet Li, Li
author_sort Li, Li
title The Normal Distribution of ω(φ(m)) in Function Fields
title_short The Normal Distribution of ω(φ(m)) in Function Fields
title_full The Normal Distribution of ω(φ(m)) in Function Fields
title_fullStr The Normal Distribution of ω(φ(m)) in Function Fields
title_full_unstemmed The Normal Distribution of ω(φ(m)) in Function Fields
title_sort normal distribution of ω(φ(m)) in function fields
publishDate 2008
url http://hdl.handle.net/10012/3567
work_keys_str_mv AT lili thenormaldistributionofōphminfunctionfields
AT lili normaldistributionofōphminfunctionfields
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