{"id":"https://openalex.org/W2137424813","doi":"https://doi.org/10.1090/mcom/3024","title":"Zeros of Dedekind zeta functions under GRH","display_name":"Zeros of Dedekind zeta functions under GRH","publication_year":2015,"publication_date":"2015-10-09","ids":{"openalex":"https://openalex.org/W2137424813","doi":"https://doi.org/10.1090/mcom/3024","mag":"2137424813"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3024","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3024","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1407.1375","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038814844","display_name":"Lo\u00efc Greni\u00e9","orcid":null},"institutions":[{"id":"https://openalex.org/I11039511","display_name":"University of Bergamo","ror":"https://ror.org/02mbd5571","country_code":"IT","type":"education","lineage":["https://openalex.org/I11039511"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Lo\u00efc Greni\u00e9","raw_affiliation_strings":["Dipartimento di Ingegneria Gestionale, dell\u2019Informazione e della Produzione, Universit\u00e0 di Bergamo, viale Marconi 5, 24044 Dalmine (BG) Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria Gestionale, dell\u2019Informazione e della Produzione, Universit\u00e0 di Bergamo, viale Marconi 5, 24044 Dalmine (BG) Italy","institution_ids":["https://openalex.org/I11039511"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002104488","display_name":"Giuseppe Molteni","orcid":"https://orcid.org/0000-0003-3323-4383"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giuseppe Molteni","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00c3\u00a0 di Milano, via Saldini 50, 20133 Milano, Italy","Dipartimento di Matematica, Universit\u00e1 di Milano, Via Saldini 50, 20133 Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00c3\u00a0 di Milano, via Saldini 50, 20133 Milano, Italy","institution_ids":["https://openalex.org/I189158943"]},{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e1 di Milano, Via Saldini 50, 20133 Milano, Italy","institution_ids":["https://openalex.org/I189158943"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6463,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.66197455,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"85","issue":"299","first_page":"1503","last_page":"1522"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":1.0,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9998000264167786,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8978593349456787},{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.8472185134887695},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.6229146122932434},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6037557125091553},{"id":"https://openalex.org/keywords/dedekind-sum","display_name":"Dedekind sum","score":0.5798929929733276},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4295574426651001},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.41129904985427856},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36639487743377686},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3246060013771057}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8978593349456787},{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.8472185134887695},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.6229146122932434},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6037557125091553},{"id":"https://openalex.org/C183606055","wikidata":"https://www.wikidata.org/wiki/Q2463775","display_name":"Dedekind sum","level":3,"score":0.5798929929733276},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4295574426651001},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.41129904985427856},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36639487743377686},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3246060013771057}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/3024","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3024","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"},{"id":"pmh:oai:arXiv.org:1407.1375","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1407.1375","pdf_url":"https://arxiv.org/pdf/1407.1375","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.766.5763","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.766.5763","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1407.1375.pdf","raw_type":"text"},{"id":"pmh:oai:aisberg.unibg.it:10446/58014","is_oa":false,"landing_page_url":"http://hdl.handle.net/10446/58014","pdf_url":null,"source":{"id":"https://openalex.org/S4377196347","display_name":"Aisberg (University of Bergamo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11039511","host_organization_name":"University of Bergamo","host_organization_lineage":["https://openalex.org/I11039511"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1407.1375","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1407.1375","pdf_url":"https://arxiv.org/pdf/1407.1375","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.41999998688697815,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1605252561","https://openalex.org/W1989563529","https://openalex.org/W1992416585","https://openalex.org/W2024731156","https://openalex.org/W2062577682","https://openalex.org/W2097199701","https://openalex.org/W2106226212","https://openalex.org/W2152890878","https://openalex.org/W2950426978","https://openalex.org/W2953109157","https://openalex.org/W3123971362"],"related_works":["https://openalex.org/W2530014757","https://openalex.org/W4300521557","https://openalex.org/W2891743814","https://openalex.org/W2027146904","https://openalex.org/W2890051578","https://openalex.org/W2229007345","https://openalex.org/W1527877675","https://openalex.org/W4300952726","https://openalex.org/W2949460333","https://openalex.org/W4296368608"],"abstract_inverted_index":{"Assuming":[0],"GRH,":[1],"we":[2],"prove":[3,61],"an":[4],"explicit":[5],"upper":[6,27,32],"bound":[7,63],"for":[8,64],"the":[9,65,68],"number":[10],"of":[11,13,67],"zeros":[12],"a":[14,30,35,62],"Dedekind":[15],"zeta":[16],"function":[17],"having":[18],"imaginary":[19],"part":[20],"in":[21],"<inline-formula":[22],"content-type=\"math/mathml\">":[23],"<mml:math":[24],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[25],"alttext=\"left-bracket":[26],"T":[28,33],"minus":[29],"comma":[31],"plus":[34],"right-bracket\">":[36],"<mml:semantics>":[37],"<mml:mrow>":[38],"<mml:mo":[39,50],"stretchy=\"false\">[</mml:mo>":[40],"<mml:mi>T</mml:mi>":[41,47],"<mml:mo>":[42],"\u2212":[43],"</mml:mo>":[44],"<mml:mi>a</mml:mi>":[45,49],"<mml:mo>,</mml:mo>":[46],"<mml:mo>+</mml:mo>":[48],"stretchy=\"false\">]</mml:mo>":[51],"</mml:mrow>":[52],"<mml:annotation":[53],"encoding=\"application/x-tex\">[T-a,T+a]</mml:annotation>":[54],"</mml:semantics>":[55],"</mml:math>":[56],"</inline-formula>":[57],".":[58],"We":[59],"also":[60],"multiplicity":[66],"zeros.":[69]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}