{"id":"https://openalex.org/W1988007980","doi":"https://doi.org/10.1090/s0025-5718-01-01305-9","title":"Localization of the first zero of the Dedekind zeta function","display_name":"Localization of the first zero of the Dedekind zeta function","publication_year":2001,"publication_date":"2001-03-07","ids":{"openalex":"https://openalex.org/W1988007980","doi":"https://doi.org/10.1090/s0025-5718-01-01305-9","mag":"1988007980"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01305-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01305-9","pdf_url":"https://www.ams.org/mcom/2001-70-236/S0025-5718-01-01305-9/S0025-5718-01-01305-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-236/S0025-5718-01-01305-9/S0025-5718-01-01305-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085908966","display_name":"Sami Omar","orcid":"https://orcid.org/0000-0002-3028-7618"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Sami Omar","raw_affiliation_strings":["Laboratoire d\u00e2\u0080\u0099Algorithmique Arithm\u00c3\u00a9tique, Universit\u00c3\u00a9 Bordeaux I, 351 cours de la Lib\u00c3\u00a9ration, F-33405 Talence Cedex France","Laboratoire d'Algorithmique Arithm\u00e9tique Universit\u00e9 Bordeaux I 351, cours de la Lib\u00e9ration F-33405 Talence Cedex, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d\u00e2\u0080\u0099Algorithmique Arithm\u00c3\u00a9tique, Universit\u00c3\u00a9 Bordeaux I, 351 cours de la Lib\u00c3\u00a9ration, F-33405 Talence Cedex France","institution_ids":[]},{"raw_affiliation_string":"Laboratoire d'Algorithmique Arithm\u00e9tique Universit\u00e9 Bordeaux I 351, cours de la Lib\u00e9ration F-33405 Talence Cedex, France","institution_ids":["https://openalex.org/I15057530"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085908966"],"corresponding_institution_ids":["https://openalex.org/I15057530"],"apc_list":null,"apc_paid":null,"fwci":0.4822,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.59607275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"236","first_page":"1607","last_page":"1616"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.9234251379966736},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8579422235488892},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.7968716621398926},{"id":"https://openalex.org/keywords/dedekind-sum","display_name":"Dedekind sum","score":0.6728789806365967},{"id":"https://openalex.org/keywords/arithmetic-zeta-function","display_name":"Arithmetic zeta function","score":0.6256998777389526},{"id":"https://openalex.org/keywords/dedekind-eta-function","display_name":"Dedekind eta function","score":0.6244122982025146},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.5685879588127136},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5375070571899414},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.5098482966423035},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5002505779266357},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4152262508869171},{"id":"https://openalex.org/keywords/modular-form","display_name":"Modular form","score":0.17787125706672668},{"id":"https://openalex.org/keywords/eisenstein-series","display_name":"Eisenstein series","score":0.06768953800201416},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.04977765679359436}],"concepts":[{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.9234251379966736},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8579422235488892},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.7968716621398926},{"id":"https://openalex.org/C183606055","wikidata":"https://www.wikidata.org/wiki/Q2463775","display_name":"Dedekind sum","level":3,"score":0.6728789806365967},{"id":"https://openalex.org/C35861355","wikidata":"https://www.wikidata.org/wiki/Q4791135","display_name":"Arithmetic zeta function","level":3,"score":0.6256998777389526},{"id":"https://openalex.org/C56357843","wikidata":"https://www.wikidata.org/wiki/Q1182161","display_name":"Dedekind eta function","level":4,"score":0.6244122982025146},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.5685879588127136},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5375070571899414},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.5098482966423035},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5002505779266357},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4152262508869171},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.17787125706672668},{"id":"https://openalex.org/C133835828","wikidata":"https://www.wikidata.org/wiki/Q1313257","display_name":"Eisenstein series","level":3,"score":0.06768953800201416},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.04977765679359436},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-01-01305-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01305-9","pdf_url":"https://www.ams.org/mcom/2001-70-236/S0025-5718-01-01305-9/S0025-5718-01-01305-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.108.2048","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.108.2048","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2001-70-236/S0025-5718-01-01305-9/S0025-5718-01-01305-9.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.3823","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.3823","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2001-70-236/S0025-5718-01-01305-9/S0025-5718-01-01305-9.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01305-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01305-9","pdf_url":"https://www.ams.org/mcom/2001-70-236/S0025-5718-01-01305-9/S0025-5718-01-01305-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.800000011920929}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1988007980.pdf","grobid_xml":"https://content.openalex.org/works/W1988007980.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1496801598","https://openalex.org/W1509814995","https://openalex.org/W1531115685","https://openalex.org/W1995178984","https://openalex.org/W2010828369","https://openalex.org/W2073732659","https://openalex.org/W2212866430","https://openalex.org/W2299769372","https://openalex.org/W2601045014","https://openalex.org/W2742529738","https://openalex.org/W2983337356","https://openalex.org/W3007836994","https://openalex.org/W3119264854","https://openalex.org/W4230941884","https://openalex.org/W4256113130","https://openalex.org/W6688359729","https://openalex.org/W6735339361"],"related_works":["https://openalex.org/W2949460333","https://openalex.org/W4298224166","https://openalex.org/W2891743814","https://openalex.org/W1977449272","https://openalex.org/W4300952726","https://openalex.org/W2890051578","https://openalex.org/W2170126841","https://openalex.org/W4289548815","https://openalex.org/W2963125920","https://openalex.org/W1988007980"],"abstract_inverted_index":{"Using":[0],"Weil\u2019s":[1],"explicit":[2],"formula,":[3],"we":[4,23],"propose":[5],"a":[6],"method":[7],"to":[8,34,44],"compute":[9,24],"low":[10],"zeros":[11],"of":[12,20,28,38],"the":[13,25,29,47],"Dedekind":[14,30],"zeta":[15,31],"function.":[16],"As":[17],"an":[18],"application":[19],"this":[21],"method,":[22],"first":[26],"zero":[27],"function":[32],"associated":[33],"totally":[35],"complex":[36],"fields":[37],"degree":[39],"less":[40],"than":[41],"or":[42],"equal":[43],"30":[45],"having":[46],"smallest":[48],"known":[49],"discriminant.":[50]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}