{"id":"https://openalex.org/W2089041583","doi":"https://doi.org/10.1007/s10998-010-1037-3","title":"A monotonicity property of Riemann\u2019s xi function and a reformulation of the Riemann hypothesis","display_name":"A monotonicity property of Riemann\u2019s xi function and a reformulation of the Riemann hypothesis","publication_year":2010,"publication_date":"2010-03-01","ids":{"openalex":"https://openalex.org/W2089041583","doi":"https://doi.org/10.1007/s10998-010-1037-3","mag":"2089041583"},"language":"en","primary_location":{"id":"doi:10.1007/s10998-010-1037-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10998-010-1037-3","pdf_url":null,"source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1005.1104","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078146626","display_name":"Jonathan Sondow","orcid":null},"institutions":[{"id":"https://openalex.org/I4210107408","display_name":"New York Proton Center","ror":"https://ror.org/01m7v2988","country_code":"US","type":"facility","lineage":["https://openalex.org/I4210107408"]},{"id":"https://openalex.org/I4210120805","display_name":"Faculty of 1000 (United States)","ror":"https://ror.org/02x5wxx17","country_code":"US","type":"company","lineage":["https://openalex.org/I4210101920","https://openalex.org/I4210120805"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jonathan Sondow","raw_affiliation_strings":["209 West 97th Street, New York, New York, 10025, USA","New York, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"209 West 97th Street, New York, New York, 10025, USA","institution_ids":["https://openalex.org/I4210120805"]},{"raw_affiliation_string":"New York, USA","institution_ids":["https://openalex.org/I4210107408"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065792274","display_name":"Cristian Dumitrescu","orcid":"https://orcid.org/0000-0003-3641-3184"},"institutions":[{"id":"https://openalex.org/I2802857469","display_name":"Emmanuel Bible College","ror":"https://ror.org/019x00e11","country_code":"CA","type":"education","lineage":["https://openalex.org/I2802857469"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Cristian Dumitrescu","raw_affiliation_strings":["119 Young Street, Kitchener, Ontario, N2H4Z3, Canada","Kitchener, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"119 Young Street, Kitchener, Ontario, N2H4Z3, Canada","institution_ids":["https://openalex.org/I2802857469"]},{"raw_affiliation_string":"Kitchener, Canada","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078146626"],"corresponding_institution_ids":["https://openalex.org/I4210107408","https://openalex.org/I4210120805"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.39,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.58140883,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"60","issue":"1","first_page":"37","last_page":"40"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9922999739646912,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9922999739646912,"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":0.9904999732971191,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9030225276947021},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.7370038628578186},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.7136019468307495},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6918949484825134},{"id":"https://openalex.org/keywords/geometric-function-theory","display_name":"Geometric function theory","score":0.5873225927352905},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5344862937927246},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5126397013664246},{"id":"https://openalex.org/keywords/riemann-sum","display_name":"Riemann sum","score":0.4950768053531647},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.485761433839798},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.480121374130249},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.473704069852829},{"id":"https://openalex.org/keywords/z-function","display_name":"Z function","score":0.4711887836456299},{"id":"https://openalex.org/keywords/riemann-xi-function","display_name":"Riemann Xi function","score":0.4594065248966217},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4319426417350769},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1519644856452942}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9030225276947021},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.7370038628578186},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.7136019468307495},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6918949484825134},{"id":"https://openalex.org/C112468886","wikidata":"https://www.wikidata.org/wiki/Q5535485","display_name":"Geometric function theory","level":3,"score":0.5873225927352905},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5344862937927246},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5126397013664246},{"id":"https://openalex.org/C189903471","wikidata":"https://www.wikidata.org/wiki/Q1156903","display_name":"Riemann sum","level":4,"score":0.4950768053531647},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.485761433839798},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.480121374130249},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.473704069852829},{"id":"https://openalex.org/C111993293","wikidata":"https://www.wikidata.org/wiki/Q8063364","display_name":"Z function","level":4,"score":0.4711887836456299},{"id":"https://openalex.org/C48902493","wikidata":"https://www.wikidata.org/wiki/Q2152235","display_name":"Riemann Xi function","level":3,"score":0.4594065248966217},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4319426417350769},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1519644856452942},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10998-010-1037-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10998-010-1037-3","pdf_url":null,"source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1005.1104","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1005.1104","pdf_url":"https://arxiv.org/pdf/1005.1104","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1005.1104","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1005.1104","pdf_url":"https://arxiv.org/pdf/1005.1104","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.4699999988079071,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W1498769399","https://openalex.org/W2492284202"],"related_works":["https://openalex.org/W2058413379","https://openalex.org/W3152426946","https://openalex.org/W2373675205","https://openalex.org/W4256540622","https://openalex.org/W2028733910","https://openalex.org/W2053341047","https://openalex.org/W3003761321","https://openalex.org/W2091817259","https://openalex.org/W4206079290","https://openalex.org/W3135547631"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2016-06-24T00:00:00"}
