{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71200"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71200","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On the Distribution Function of N/phi(n)","abstract":"Let (phi)(n) denote Euler's function and let D(x) denote the distribution function of","abstract_html":"Let (phi)(n) denote Euler's function and let D(x) denote the distribution function of","abstract_has_math":false,"creators":["Rhoads, Dennis Lynn"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T06:18:02Z","date_published":"2014-12-16T06:18:02Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8203565"],"render_values":[{"text":"(UMI)AAI8203565","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71200","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Rhoads, Dennis Lynn"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:02Z","10000-01-01","1981"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71200","(UMI)AAI8203565"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Let (phi)(n) denote Euler's function and let D(x) denote the distribution function of","(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)","i.e.,","A method is developed for numerically approximating D(x) based on a series expansion of D(x).","An estimate of the modulus of continuity of D(x) is also established. In this regard, the following result is established.","Theorem. There exists an absolute constant c such that for 0 0 we have","D(x+(epsilon)x) - D(x) < c/log(1/(epsilon)).","Made available in DSpace on 2014-12-16T06:18:02Z (GMT). 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In this regard, the following result is established.","Theorem. There exists an absolute constant c such that for 0 0 we have","D(x+(epsilon)x) - D(x) < c/log(1/(epsilon)).","Made available in DSpace on 2014-12-16T06:18:02Z (GMT). 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