{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86886"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86886","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Congruence Properties of Fourier Coefficients of Modular Forms","abstract":"Fourier coefficients of modular forms have profound connections with many areas of number theory. We will consider three different applications of these coefficients. First, we extend the Apery number supercongruence, proving an observation of Rodriguez-Villegas. Second, we prove an analogue of Newman's Conjecture with prime-power moduli for a class of partition functions. Finally, we prove some results about the integrality of Fourier coefficients of cusp forms at cusps other than infinity.","abstract_html":"Fourier coefficients of modular forms have profound connections with many areas of number theory. We will consider three different applications of these coefficients. First, we extend the Apery number supercongruence, proving an observation of Rodriguez-Villegas. Second, we prove an analogue of Newman's Conjecture with prime-power moduli for a class of partition functions. Finally, we prove some results about the integrality of Fourier coefficients of cusp forms at cusps other than infinity.","abstract_has_math":false,"creators":["Kilbourn, Timothy"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Ahlgren, Scott"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:20:00Z","date_published":"2015-09-28T15:20:00Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3290272"],"render_values":[{"text":"(MiAaPQ)AAI3290272","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86886","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ahlgren, Scott"]},{"key":"dc:creator","label":"Author","values":["Kilbourn, Timothy"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:00Z","10000-01-01","2007"]},{"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":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86886","(MiAaPQ)AAI3290272"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Fourier coefficients of modular forms have profound connections with many areas of number theory. We will consider three different applications of these coefficients. First, we extend the Apery number supercongruence, proving an observation of Rodriguez-Villegas. Second, we prove an analogue of Newman's Conjecture with prime-power moduli for a class of partition functions. Finally, we prove some results about the integrality of Fourier coefficients of cusp forms at cusps other than infinity.","Made available in DSpace on 2015-09-28T15:20:00Z (GMT). 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First, we extend the Apery number supercongruence, proving an observation of Rodriguez-Villegas. Second, we prove an analogue of Newman's Conjecture with prime-power moduli for a class of partition functions. Finally, we prove some results about the integrality of Fourier coefficients of cusp forms at cusps other than infinity.","Made available in DSpace on 2015-09-28T15:20:00Z (GMT). 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