Date of Award

January 2015

Degree Type

Open Access Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics and Statistics

First Advisor

Donald Jason Gibson

Department Affiliation

Mathematics and Statistics

Second Advisor

Lisa Whitis Kay

Department Affiliation

Mathematics and Statistics

Third Advisor

Rachel Bishop-Ross

Department Affiliation

Mathematics and Statistics

Abstract

The Erd\H{o}-Kac Theorem states that, as $n$ tends to infinity, the distribution of $\omega(n)$, the number of distinct prime divisors of $n$, becomes normally distributed with mean and variance $\log\log n$. Granville and Soundararajan gave a proof of the Erd\H{o}s-Kac Theorem that avoided many of the specialized techniques present in several earlier approaches. This thesis includes considerable detail, prerequisite theorems, and instructive background in order to provide a self-contained exposition of the proof of Granville and Soundararajan.

Included in

Mathematics Commons

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