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.
","abstract_html":"<p>The Erd\\H{o}-Kac Theorem states that, as $n$ tends to infinity, the distribution of ω(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. </p>","abstract_has_math":true,"creators":["Scheithauer, Thomas John"],"institution":"Eastern Kentucky University","degree_name":"Master of Arts (MA)","degree_level":"Master's","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-01T08:00:00Z","date_published":"2015-01-01T08:00:00Z","updated_at":"2026-07-24T02:15:39Z","subjects":["Distribution","Divisor","Erdos","Kac","Normal","Prime","Mathematics"],"languages":[],"rights":["Copyright 2015 Thomas John Scheithauer"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://encompass.eku.edu/etd/422","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Scheithauer, Thomas John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Encompass Digital Archive, Eastern Kentucky University"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts (MA)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Eastern Kentucky University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Distribution","Divisor","Erdos","Kac","Normal","Prime","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2015 Thomas John Scheithauer"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://encompass.eku.edu/etd/422"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
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"],"dc:format":["application/pdf"],"dc:identifier":["https://encompass.eku.edu/etd/422"],"dc:publisher":["Encompass Digital Archive, Eastern Kentucky University"],"dc:rights":["Copyright 2015 Thomas John Scheithauer"],"dc:source":["Encompass Digital Archive: Online Theses and Dissertations"],"dc:subject":["Distribution","Divisor","Erdos","Kac","Normal","Prime","Mathematics"],"dc:title":["A Thorough and Accessible Proof of the Erdo˝s-Kac Theorem Following Granville and Soundararajan"],"dc:type":["Master Thesis"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Arts (MA)"],"thesis:institution_name":["Eastern Kentucky University"]},"updated_at":"2026-07-24T02:15:39Z"}