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

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.

Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OWTU.10012/3567
Date January 2007
CreatorsLi, Li
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation

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