{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/120085"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/120085","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Topics in analytic number theory","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms","abstract_has_math":false,"creators":["Jaffe, Grace Natalie"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Reznick, Bruce","Zaharescu, Alexandru","Berndt, Bruce C","Nath, Kunjakanan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-05","date_published":"2023-05","updated_at":"2026-07-22T22:24:56Z","subjects":["Number Theory","Frobenius Problem","Stern Sequence","Farey Sequences","Dirichlet L-function","Riemann Zeta Function"],"languages":["en","eng"],"rights":["Copyright 2023 Grace Jaffe"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/120085","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Reznick, Bruce","Zaharescu, Alexandru","Berndt, Bruce C","Nath, Kunjakanan"]},{"key":"dc:creator","label":"Author","values":["Jaffe, Grace Natalie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-05","2023-04-28"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"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":["Number Theory","Frobenius Problem","Stern Sequence","Farey Sequences","Dirichlet L-function","Riemann Zeta Function"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2023 Grace Jaffe"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/120085"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms","The student, Grace Jaffe, accepted the attached license on 2023-04-23 at 20:17.","The student, Grace Jaffe, submitted this Dissertation for approval on 2023-04-23 at 20:29.","This Dissertation was approved for publication on 2023-04-28 at 09:08.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19123 on 2023-09-01 at 16:55:08","In Part I of this thesis, we show that for relatively prime positive integers a,b, there is a maximum integer g(a,b) which is not expressible as ax+by for x,y non-negative, relatively prime integers. We then explore the connections between this quantity and the Frobenius problem, Farey sequence, and Stern sequence. In Part II, we consider the zeros of a polynomial in derivatives of a Dirichlet L-function and give an asymptotic formula for the number of zeros with imaginary part between 1 and large T."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Topics in analytic number theory"]}]}],"canonical_facts":{"dc:contributor":["Reznick, Bruce","Zaharescu, Alexandru","Berndt, Bruce C","Nath, Kunjakanan"],"dc:creator":["Jaffe, Grace Natalie"],"dc:date":["2023-05","2023-04-28"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms","The student, Grace Jaffe, accepted the attached license on 2023-04-23 at 20:17.","The student, Grace Jaffe, submitted this Dissertation for approval on 2023-04-23 at 20:29.","This Dissertation was approved for publication on 2023-04-28 at 09:08.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19123 on 2023-09-01 at 16:55:08","In Part I of this thesis, we show that for relatively prime positive integers a,b, there is a maximum integer g(a,b) which is not expressible as ax+by for x,y non-negative, relatively prime integers. We then explore the connections between this quantity and the Frobenius problem, Farey sequence, and Stern sequence. In Part II, we consider the zeros of a polynomial in derivatives of a Dirichlet L-function and give an asymptotic formula for the number of zeros with imaginary part between 1 and large T."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/120085"],"dc:language":["en","eng"],"dc:rights":["Copyright 2023 Grace Jaffe"],"dc:subject":["Number Theory","Frobenius Problem","Stern Sequence","Farey Sequences","Dirichlet L-function","Riemann Zeta Function"],"dc:title":["Topics in analytic number theory"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:56Z"}