{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/127304"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/127304","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Sturm sequences of polynomials related to regular primes","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-03-28 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-03-28 without embargo terms","abstract_has_math":false,"creators":["Robinson, Malachi M."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Ahlgren, Scott"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-12-13","date_published":"2024-12-13","updated_at":"2026-07-22T22:25:03Z","subjects":["Sturm Sequence"],"languages":["en","eng"],"rights":["Copyright 2024 Malachi Robinson"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/127304","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ahlgren, Scott"]},{"key":"dc:creator","label":"Author","values":["Robinson, Malachi M."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-12-13","2024-12"]},{"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":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["Sturm Sequence"]}]},{"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 2024 Malachi Robinson"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/127304"]}]},{"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 2025-03-28 without embargo terms","The student, Malachi Robinson, accepted the attached license on 2024-12-13 at 11:37.","The student, Malachi Robinson, submitted this Thesis for approval on 2024-12-13 at 11:43.","This Thesis was approved for publication on 2024-12-13 at 14:46.","DSpace SAF Submission Ingestion Package generated from Vireo submission #21597 on 2025-03-28 at 14:28:54","We discuss Kummer’s algebraic definition of a regular prime number p involving the class number of the cyclotomic field Q(ζp) and Kummer’s criterion for a prime number to be regular, which involves the numerators of Bernoulli numbers. A discussion of Sturm sequences and a software implementation follows. We conjecture and provide strong evidence for an integer upper and lower bound, [k − 4 k 5, k − 4 k 6] for the number of real roots of the kth Bernoulli polynomial using data generated by computing Sturm sequences. We then prove explicit formulae for each of the terms of the Sturm sequences of cyclotomic polynomials Φn(x), where n is a prime greater than 3 or a power of 2."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Sturm sequences of polynomials related to regular primes"]}]}],"canonical_facts":{"dc:contributor":["Ahlgren, Scott"],"dc:creator":["Robinson, Malachi M."],"dc:date":["2024-12-13","2024-12"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-03-28 without embargo terms","The student, Malachi Robinson, accepted the attached license on 2024-12-13 at 11:37.","The student, Malachi Robinson, submitted this Thesis for approval on 2024-12-13 at 11:43.","This Thesis was approved for publication on 2024-12-13 at 14:46.","DSpace SAF Submission Ingestion Package generated from Vireo submission #21597 on 2025-03-28 at 14:28:54","We discuss Kummer’s algebraic definition of a regular prime number p involving the class number of the cyclotomic field Q(ζp) and Kummer’s criterion for a prime number to be regular, which involves the numerators of Bernoulli numbers. A discussion of Sturm sequences and a software implementation follows. We conjecture and provide strong evidence for an integer upper and lower bound, [k − 4 k 5, k − 4 k 6] for the number of real roots of the kth Bernoulli polynomial using data generated by computing Sturm sequences. We then prove explicit formulae for each of the terms of the Sturm sequences of cyclotomic polynomials Φn(x), where n is a prime greater than 3 or a power of 2."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/127304"],"dc:language":["en","eng"],"dc:rights":["Copyright 2024 Malachi Robinson"],"dc:subject":["Sturm Sequence"],"dc:title":["Sturm sequences of polynomials related to regular primes"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:03Z"}