{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/22301"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/22301","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms","abstract":"\"In the first part of this thesis, we prove Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms. We prove his formulas for the coefficients of 1/$E\\sb4, E\\sb4/E\\sb6$ and other functions involving the Eisenstein series $E\\sb4, E\\sb6$ and $E\\sbsp{2}{*}$. These formulas are stated, without proof, in a three-page manuscript published with his \"\"lost notebook.\"\"\"","abstract_html":""In the first part of this thesis, we prove Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms. We prove his formulas for the coefficients of 1/$E\\sb4, E\\sb4/E\\sb6$ and other functions involving the Eisenstein series $E\\sb4, E\\sb6$ and $E\\sbsp{2}{*}$. These formulas are stated, without proof, in a three-page manuscript published with his ""lost notebook."""","abstract_has_math":true,"creators":["Bialek, Paul Richard"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Berndt, Bruce C."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:35:30Z","date_published":"2011-05-07T13:35:30Z","updated_at":"2026-07-22T22:25:19Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1995 Bialek, Paul Richard"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9522080","(UMI)AAI9522080"],"render_values":[{"text":"AAI9522080","href":null,"code":true},{"text":"(UMI)AAI9522080","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/22301","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Berndt, Bruce C."]},{"key":"dc:creator","label":"Author","values":["Bialek, Paul Richard"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:35:30Z","10000-01-01","1995"]},{"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"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1995 Bialek, Paul Richard"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9522080","(UMI)AAI9522080","http://hdl.handle.net/2142/22301"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"In the first part of this thesis, we prove Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms. We prove his formulas for the coefficients of 1/$E\\sb4, E\\sb4/E\\sb6$ and other functions involving the Eisenstein series $E\\sb4, E\\sb6$ and $E\\sbsp{2}{*}$. These formulas are stated, without proof, in a three-page manuscript published with his \"\"lost notebook.\"\"\"","In the second part of this thesis, we prove five series identities of Ramanujan which arise from Eisenstein series. These identities are stated, without proof, in the unorganized portion of his second notebook.","Made available in DSpace on 2011-05-07T13:35:30Z (GMT). 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We prove his formulas for the coefficients of 1/$E\\sb4, E\\sb4/E\\sb6$ and other functions involving the Eisenstein series $E\\sb4, E\\sb6$ and $E\\sbsp{2}{*}$. These formulas are stated, without proof, in a three-page manuscript published with his \"\"lost notebook.\"\"\"","In the second part of this thesis, we prove five series identities of Ramanujan which arise from Eisenstein series. These identities are stated, without proof, in the unorganized portion of his second notebook.","Made available in DSpace on 2011-05-07T13:35:30Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9522080.pdf: 3513664 bytes, checksum: 089f5dfe3bd80cbe0663d4e1dfe62086 (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:56:41Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:26:31-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9522080","(UMI)AAI9522080","http://hdl.handle.net/2142/22301"],"dc:language":["eng"],"dc:rights":["Copyright 1995 Bialek, Paul Richard"],"dc:subject":["Mathematics"],"dc:title":["Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:19Z"}