{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71263"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71263","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Analytic Continuation and Functional Equations of Cuspidal Eisenstein Series for Maximal Cuspidal Subgroups","abstract":"In this work we develop an approach of Selberg to the analytic continuation of Eisenstein series by means of Fredholm theory. We set up the machinery for very general algebraic groups and arithmetic subgroups, and obtain the analytic continuation and functional equations of cuspidal Eisenstein series for rank one cuspidal subgroups. This approach suggests an alternative development to part of Langlands' theory of Eisenstein series. It also opens up the possibility of more precise knowledge about the poles of Eisenstein series.","abstract_html":"In this work we develop an approach of Selberg to the analytic continuation of Eisenstein series by means of Fredholm theory. We set up the machinery for very general algebraic groups and arithmetic subgroups, and obtain the analytic continuation and functional equations of cuspidal Eisenstein series for rank one cuspidal subgroups. This approach suggests an alternative development to part of Langlands' theory of Eisenstein series. It also opens up the possibility of more precise knowledge about the poles of Eisenstein series.","abstract_has_math":false,"creators":["Wong, Shek-Tung"],"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":"2014-12-16T06:18:21Z","date_published":"2014-12-16T06:18:21Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8803240"],"render_values":[{"text":"(UMI)AAI8803240","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71263","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Wong, Shek-Tung"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:21Z","10000-01-01","1987"]},{"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/2142/71263","(UMI)AAI8803240"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this work we develop an approach of Selberg to the analytic continuation of Eisenstein series by means of Fredholm theory. We set up the machinery for very general algebraic groups and arithmetic subgroups, and obtain the analytic continuation and functional equations of cuspidal Eisenstein series for rank one cuspidal subgroups. This approach suggests an alternative development to part of Langlands' theory of Eisenstein series. It also opens up the possibility of more precise knowledge about the poles of Eisenstein series.","Made available in DSpace on 2014-12-16T06:18:21Z (GMT). No. of bitstreams: 1 8803240.pdf: 5018898 bytes, checksum: f5c9afe171f37f22314bf4a527722315 (MD5) Previous issue date: 1987","Embargo set by: Seth Robbins for item 71429 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","209 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987."]},{"key":"dc:title","label":"Title","values":["Analytic Continuation and Functional Equations of Cuspidal Eisenstein Series for Maximal Cuspidal Subgroups"]}]}],"canonical_facts":{"dc:creator":["Wong, Shek-Tung"],"dc:date":["2014-12-16T06:18:21Z","10000-01-01","1987"],"dc:description":["In this work we develop an approach of Selberg to the analytic continuation of Eisenstein series by means of Fredholm theory. We set up the machinery for very general algebraic groups and arithmetic subgroups, and obtain the analytic continuation and functional equations of cuspidal Eisenstein series for rank one cuspidal subgroups. This approach suggests an alternative development to part of Langlands' theory of Eisenstein series. It also opens up the possibility of more precise knowledge about the poles of Eisenstein series.","Made available in DSpace on 2014-12-16T06:18:21Z (GMT). No. of bitstreams: 1 8803240.pdf: 5018898 bytes, checksum: f5c9afe171f37f22314bf4a527722315 (MD5) Previous issue date: 1987","Embargo set by: Seth Robbins for item 71429 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","209 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987."],"dc:identifier":["http://hdl.handle.net/2142/71263","(UMI)AAI8803240"],"dc:subject":["Mathematics"],"dc:title":["Analytic Continuation and Functional Equations of Cuspidal Eisenstein Series for Maximal Cuspidal Subgroups"],"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":"2026-07-22T22:26:04Z"}