{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86972"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86972","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook","abstract":"S. Ramanujan's last letter to G. H. Hardy contains the definition of mock theta functions, a list of 17 mock theta functions, and 5 identities related to mock theta functions. Also, Ramanujan's lost notebook contains many further results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions which heretofore have not been proved. It is the purpose of this thesis to prove the first four of Ramanujan's tenth order mock theta function identities. Although in this paper the Bailey pair method developed by G. E. Andrews and the constant term method developed by D. Hickerson are playing key roles, the other main idea is transforming mock theta function identities into the theta function identities.","abstract_html":"S. Ramanujan's last letter to G. H. Hardy contains the definition of mock theta functions, a list of 17 mock theta functions, and 5 identities related to mock theta functions. Also, Ramanujan's lost notebook contains many further results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions which heretofore have not been proved. It is the purpose of this thesis to prove the first four of Ramanujan's tenth order mock theta function identities. Although in this paper the Bailey pair method developed by G. E. Andrews and the constant term method developed by D. Hickerson are playing key roles, the other main idea is transforming mock theta function identities into the theta function identities.","abstract_has_math":false,"creators":["Choi, Youn-Seo"],"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":2015,"date_issued":"2015-09-28T15:20:25Z","date_published":"2015-09-28T15:20:25Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI9944820"],"render_values":[{"text":"(MiAaPQ)AAI9944820","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86972","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":["Choi, Youn-Seo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:25Z","10000-01-01","1999"]},{"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/2142/86972","(MiAaPQ)AAI9944820"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["S. Ramanujan's last letter to G. H. Hardy contains the definition of mock theta functions, a list of 17 mock theta functions, and 5 identities related to mock theta functions. Also, Ramanujan's lost notebook contains many further results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions which heretofore have not been proved. It is the purpose of this thesis to prove the first four of Ramanujan's tenth order mock theta function identities. Although in this paper the Bailey pair method developed by G. E. Andrews and the constant term method developed by D. Hickerson are playing key roles, the other main idea is transforming mock theta function identities into the theta function identities.","Made available in DSpace on 2015-09-28T15:20:25Z (GMT). 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Also, Ramanujan's lost notebook contains many further results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions which heretofore have not been proved. It is the purpose of this thesis to prove the first four of Ramanujan's tenth order mock theta function identities. Although in this paper the Bailey pair method developed by G. E. Andrews and the constant term method developed by D. Hickerson are playing key roles, the other main idea is transforming mock theta function identities into the theta function identities.","Made available in DSpace on 2015-09-28T15:20:25Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9944820.pdf: 5769380 bytes, checksum: 8ed246a6af746fe263bce1a0efef3a56 (MD5) Previous issue date: 1999","Embargo set by: Seth Robbins for item 88253 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","175 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999."],"dc:identifier":["http://hdl.handle.net/2142/86972","(MiAaPQ)AAI9944820"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook"],"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":"2026-07-22T22:26:28Z"}