{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/68175"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/68175","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Improvements in the Small Sieve Estimate of Selberg by Iteration","abstract":"In the notation of H. Halberstam and H.-E. Richert, the small sieve estimate of Selberg is","abstract_html":"In the notation of H. Halberstam and H.-E. Richert, the small sieve estimate of Selberg is","abstract_has_math":false,"creators":["Rawsthorne, Daniel Andrew"],"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":"2014-12-14T13:09:47Z","date_published":"2014-12-14T13:09:47Z","updated_at":"2026-07-22T22:25:58Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8026575"],"render_values":[{"text":"(UMI)AAI8026575","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/68175","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Rawsthorne, Daniel Andrew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-14T13:09:47Z","10000-01-01","1980"]},{"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/2142/68175","(UMI)AAI8026575"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In the notation of H. Halberstam and H.-E. Richert, the small sieve estimate of Selberg is","(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)","where (tau) = log (xi)('2)/log z. Repeated iteration of (*) with the Buchstab identity produces improved upper (and lower) bounds for ( ; ,z). Sieve results of the form (*) are produced for each intermediate function produced by iteration, and also for the limit functions approached.","The limit functions are solutions of a pair of difference-differential equations, and Laplace transform methods are used in an effort to define the functions analytically. Two curves are produced such that the coordinates of one of their intersections are the two parameters that need to be found. Computer calculations indicate that there is in fact a unique intersection, but this is not proved; and by assuming the intersection is unique, approximate values of the parameters are given for various dimensions.","In addition to the above work, it is also shown that the L in the 0-term of (*) is unnecessary; and the iteration is studied when one begins with a general "upper bound function" (defined in the paper).","Made available in DSpace on 2014-12-14T13:09:47Z (GMT). No. of bitstreams: 1 8026575.pdf: 2449244 bytes, checksum: 4dd6b50c023cb13d7792e6f3222a9d40 (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 68353 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","107 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."]},{"key":"dc:title","label":"Title","values":["Improvements in the Small Sieve Estimate of Selberg by Iteration"]}]}],"canonical_facts":{"dc:creator":["Rawsthorne, Daniel Andrew"],"dc:date":["2014-12-14T13:09:47Z","10000-01-01","1980"],"dc:description":["In the notation of H. Halberstam and H.-E. Richert, the small sieve estimate of Selberg is","(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)","where (tau) = log (xi)('2)/log z. Repeated iteration of (*) with the Buchstab identity produces improved upper (and lower) bounds for ( ; ,z). Sieve results of the form (*) are produced for each intermediate function produced by iteration, and also for the limit functions approached.","The limit functions are solutions of a pair of difference-differential equations, and Laplace transform methods are used in an effort to define the functions analytically. Two curves are produced such that the coordinates of one of their intersections are the two parameters that need to be found. Computer calculations indicate that there is in fact a unique intersection, but this is not proved; and by assuming the intersection is unique, approximate values of the parameters are given for various dimensions.","In addition to the above work, it is also shown that the L in the 0-term of (*) is unnecessary; and the iteration is studied when one begins with a general "upper bound function" (defined in the paper).","Made available in DSpace on 2014-12-14T13:09:47Z (GMT). No. of bitstreams: 1 8026575.pdf: 2449244 bytes, checksum: 4dd6b50c023cb13d7792e6f3222a9d40 (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 68353 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","107 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."],"dc:identifier":["http://hdl.handle.net/2142/68175","(UMI)AAI8026575"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["Improvements in the Small Sieve Estimate of Selberg by Iteration"],"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":"2026-07-22T22:25:58Z"}