{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86834"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86834","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Analytic Computation of the Prime -Counting Function","abstract":"Our work resolves many issues left untreated in the original paper by Lagarias and Odlyzko and makes several original contributions---some of which have applications in other areas. In this dissertation we: (1) introduce a kernel function which appears to be more effective than the one suggested by Lagarias and Odlyzko; (2) perform a careful analysis of various sources of truncation error; (3) give choices of parameters which bound the truncation error while keeping computation to a minimum; (4) develop two new methods for enumerating primes in intervals, which require much less memory than previously known sieving methods and which are much faster than methods which test primality of single numbers; (5) describe a new method for computing zeta(s) which gives more accurate values with less complexity than classical methods.","abstract_html":"Our work resolves many issues left untreated in the original paper by Lagarias and Odlyzko and makes several original contributions---some of which have applications in other areas. In this dissertation we: (1) introduce a kernel function which appears to be more effective than the one suggested by Lagarias and Odlyzko; (2) perform a careful analysis of various sources of truncation error; (3) give choices of parameters which bound the truncation error while keeping computation to a minimum; (4) develop two new methods for enumerating primes in intervals, which require much less memory than previously known sieving methods and which are much faster than methods which test primality of single numbers; (5) describe a new method for computing zeta(s) which gives more accurate values with less complexity than classical methods.","abstract_has_math":false,"creators":["Galway, William Floyd"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Diamond, Harold G."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:46Z","date_published":"2015-09-28T15:19:46Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Computer Science"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3153295"],"render_values":[{"text":"(MiAaPQ)AAI3153295","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86834","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Diamond, Harold G."]},{"key":"dc:creator","label":"Author","values":["Galway, William Floyd"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:46Z","10000-01-01","2004"]},{"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":["Computer Science"]}]},{"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/2142/86834","(MiAaPQ)AAI3153295"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Our work resolves many issues left untreated in the original paper by Lagarias and Odlyzko and makes several original contributions---some of which have applications in other areas. In this dissertation we: (1) introduce a kernel function which appears to be more effective than the one suggested by Lagarias and Odlyzko; (2) perform a careful analysis of various sources of truncation error; (3) give choices of parameters which bound the truncation error while keeping computation to a minimum; (4) develop two new methods for enumerating primes in intervals, which require much less memory than previously known sieving methods and which are much faster than methods which test primality of single numbers; (5) describe a new method for computing zeta(s) which gives more accurate values with less complexity than classical methods.","Made available in DSpace on 2015-09-28T15:19:46Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3153295.pdf: 8063101 bytes, checksum: d8fb0799320684bbfb9494a1efc4a3e8 (MD5) Previous issue date: 2004","Embargo set by: Seth Robbins for item 88115 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","173 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004."]},{"key":"dc:title","label":"Title","values":["Analytic Computation of the Prime -Counting Function"]}]}],"canonical_facts":{"dc:contributor":["Diamond, Harold G."],"dc:creator":["Galway, William Floyd"],"dc:date":["2015-09-28T15:19:46Z","10000-01-01","2004"],"dc:description":["Our work resolves many issues left untreated in the original paper by Lagarias and Odlyzko and makes several original contributions---some of which have applications in other areas. In this dissertation we: (1) introduce a kernel function which appears to be more effective than the one suggested by Lagarias and Odlyzko; (2) perform a careful analysis of various sources of truncation error; (3) give choices of parameters which bound the truncation error while keeping computation to a minimum; (4) develop two new methods for enumerating primes in intervals, which require much less memory than previously known sieving methods and which are much faster than methods which test primality of single numbers; (5) describe a new method for computing zeta(s) which gives more accurate values with less complexity than classical methods.","Made available in DSpace on 2015-09-28T15:19:46Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3153295.pdf: 8063101 bytes, checksum: d8fb0799320684bbfb9494a1efc4a3e8 (MD5) Previous issue date: 2004","Embargo set by: Seth Robbins for item 88115 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","173 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004."],"dc:identifier":["http://hdl.handle.net/2142/86834","(MiAaPQ)AAI3153295"],"dc:language":["eng"],"dc:subject":["Computer Science"],"dc:title":["Analytic Computation of the Prime -Counting Function"],"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"}