{"id":"https://openalex.org/W2005537231","doi":"https://doi.org/10.1090/s0025-5718-07-01999-0","title":"Zeros of the Davenport-Heilbronn counterexample","display_name":"Zeros of the Davenport-Heilbronn counterexample","publication_year":2007,"publication_date":"2007-05-09","ids":{"openalex":"https://openalex.org/W2005537231","doi":"https://doi.org/10.1090/s0025-5718-07-01999-0","mag":"2005537231"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-07-01999-0","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01999-0","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023284667","display_name":"Eugenio P. Balanzario","orcid":"https://orcid.org/0000-0001-7206-7624"},"institutions":[{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Eugenio Balanzario","raw_affiliation_strings":["Instituto de Matem\u00c3\u00a1ticas, Unidad Morelia, Universidad Nacional Aut\u00c3\u00b3noma de M\u00c3\u00a9xico, Apartado Postal 61-3 (Xangari), 58089, Morelia Michoac\u00c3\u00a1n, M\u00c3\u00a9xico","Instituto de Matem\u00e1ticas, Unidad Morelia, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apartado Postal 61-3 (Xangari), 58089, Morelia Michoac\u00e1n, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00c3\u00a1ticas, Unidad Morelia, Universidad Nacional Aut\u00c3\u00b3noma de M\u00c3\u00a9xico, Apartado Postal 61-3 (Xangari), 58089, Morelia Michoac\u00c3\u00a1n, M\u00c3\u00a9xico","institution_ids":[]},{"raw_affiliation_string":"Instituto de Matem\u00e1ticas, Unidad Morelia, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apartado Postal 61-3 (Xangari), 58089, Morelia Michoac\u00e1n, Mexico","institution_ids":["https://openalex.org/I8961855"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073102768","display_name":"Jorge S\u00e1nchez-Ortiz","orcid":"https://orcid.org/0000-0002-9228-7285"},"institutions":[{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Jorge S\u00e1nchez-Ortiz","raw_affiliation_strings":["Instituto de Matem\u00c3\u00a1ticas, Unidad Morelia, Universidad Nacional Aut\u00c3\u00b3noma de M\u00c3\u00a9xico, Apartado Postal 61-3 (Xangari), 58089, Morelia Michoac\u00c3\u00a1n, M\u00c3\u00a9xico","Instituto de Matem\u00e1ticas, Unidad Morelia, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apartado Postal 61-3 (Xangari), 58089, Morelia Michoac\u00e1n, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00c3\u00a1ticas, Unidad Morelia, Universidad Nacional Aut\u00c3\u00b3noma de M\u00c3\u00a9xico, Apartado Postal 61-3 (Xangari), 58089, Morelia Michoac\u00c3\u00a1n, M\u00c3\u00a9xico","institution_ids":[]},{"raw_affiliation_string":"Instituto de Matem\u00e1ticas, Unidad Morelia, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apartado Postal 61-3 (Xangari), 58089, Morelia Michoac\u00e1n, Mexico","institution_ids":["https://openalex.org/I8961855"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I8961855"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.09929151,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"76","issue":"260","first_page":"2045","last_page":"2049"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9995999932289124,"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":0.9993000030517578,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/counterexample","display_name":"Counterexample","score":0.8693079948425293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8582772016525269},{"id":"https://openalex.org/keywords/dirichlet-series","display_name":"Dirichlet series","score":0.665891706943512},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6193211078643799},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5795359015464783},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45376622676849365},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.4216890335083008},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.3766067922115326},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37151843309402466},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16788721084594727},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11023885011672974},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06933417916297913},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05118545889854431}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.8693079948425293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8582772016525269},{"id":"https://openalex.org/C207803063","wikidata":"https://www.wikidata.org/wiki/Q620595","display_name":"Dirichlet series","level":4,"score":0.665891706943512},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6193211078643799},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5795359015464783},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45376622676849365},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4216890335083008},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.3766067922115326},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37151843309402466},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16788721084594727},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11023885011672974},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06933417916297913},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05118545889854431},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-07-01999-0","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01999-0","pdf_url":null,"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1973179387","https://openalex.org/W1996486904","https://openalex.org/W2069384709"],"related_works":["https://openalex.org/W2349952486","https://openalex.org/W1489260687","https://openalex.org/W2775700832","https://openalex.org/W3204670144","https://openalex.org/W2163101548","https://openalex.org/W1988934358","https://openalex.org/W4286908302","https://openalex.org/W2012867998","https://openalex.org/W4255421128","https://openalex.org/W2056307394"],"abstract_inverted_index":{"We":[0],"compute":[1],"zeros":[2,32],"off":[3],"the":[4,34],"critical":[5],"line":[6],"of":[7,30],"a":[8,24,28],"Dirichlet":[9,25],"series":[10,26],"considered":[11],"by":[12,22],"H.":[13,16],"Davenport":[14],"and":[15],"Heilbronn.":[17],"This":[18],"computation":[19],"is":[20],"accomplished":[21],"deforming":[23],"with":[27],"set":[29],"known":[31],"into":[33],"Davenport-Heilbronn":[35],"series.":[36]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
