{"id":"https://openalex.org/W1507390359","doi":"https://doi.org/10.1090/s0025-5718-2015-02930-5","title":"A still sharper region where \ud835\udf0b(\ud835\udc65)-fc(r) is positive","display_name":"A still sharper region where \ud835\udf0b(\ud835\udc65)-fc(r) is positive","publication_year":2015,"publication_date":"2015-02-12","ids":{"openalex":"https://openalex.org/W1507390359","doi":"https://doi.org/10.1090/s0025-5718-2015-02930-5","mag":"1507390359"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2015-02930-5","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2015-02930-5","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/A5086827489","display_name":"Yannick Saouter","orcid":"https://orcid.org/0000-0001-7980-9168"},"institutions":[{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]},{"id":"https://openalex.org/I205703379","display_name":"Institut Mines-T\u00e9l\u00e9com","ror":"https://ror.org/025vp2923","country_code":"FR","type":"facility","lineage":["https://openalex.org/I205703379"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Yannick Saouter","raw_affiliation_strings":["Institut Telecom Brest, Department Informatique, CS 83818, 29238 Brest, Cedex 3 France","Lab-STICC_TB_CACS_IAS (France)","ELEC - D\u00e9partement Electronique (Technop\u00f4le Brest-Iroise CS 83818 29238 BREST CEDEX 3 - France)"],"affiliations":[{"raw_affiliation_string":"Institut Telecom Brest, Department Informatique, CS 83818, 29238 Brest, Cedex 3 France","institution_ids":["https://openalex.org/I205703379"]},{"raw_affiliation_string":"Lab-STICC_TB_CACS_IAS (France)","institution_ids":["https://openalex.org/I161929037"]},{"raw_affiliation_string":"ELEC - D\u00e9partement Electronique (Technop\u00f4le Brest-Iroise CS 83818 29238 BREST CEDEX 3 - France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022560324","display_name":"Timothy S. Trudgian","orcid":"https://orcid.org/0000-0003-4936-7375"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I2802631561","display_name":"Australian Mathematical Sciences Institute","ror":"https://ror.org/00yn60108","country_code":"AU","type":"other","lineage":["https://openalex.org/I2802631561"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Timothy Trudgian","raw_affiliation_strings":["The Australian National University, Mathematical Sciences Institute, Building 27, ACTON, ACT 0200 Australia","ANU - Australian National University (The Australian National University Canberra ACT 0200 Australia - Australia)"],"affiliations":[{"raw_affiliation_string":"The Australian National University, Mathematical Sciences Institute, Building 27, ACTON, ACT 0200 Australia","institution_ids":["https://openalex.org/I2802631561","https://openalex.org/I118347636"]},{"raw_affiliation_string":"ANU - Australian National University (The Australian National University Canberra ACT 0200 Australia - Australia)","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028503636","display_name":"Patrick Demichel","orcid":null},"institutions":[{"id":"https://openalex.org/I1324840837","display_name":"Hewlett-Packard (United States)","ror":"https://ror.org/059rn9488","country_code":"US","type":"company","lineage":["https://openalex.org/I1324840837"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patrick Demichel","raw_affiliation_strings":["Hewlett-Packard France, 91947 Les Ulis, Cedex France","Hewlett-Packard (United States)"],"affiliations":[{"raw_affiliation_string":"Hewlett-Packard France, 91947 Les Ulis, Cedex France","institution_ids":["https://openalex.org/I1324840837"]},{"raw_affiliation_string":"Hewlett-Packard (United States)","institution_ids":["https://openalex.org/I1324840837"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086827489"],"corresponding_institution_ids":["https://openalex.org/I161929037","https://openalex.org/I205703379"],"apc_list":null,"apc_paid":null,"fwci":2.0169,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.82282609,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"84","issue":"295","first_page":"2433","last_page":"2446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","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"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.8220101594924927},{"id":"https://openalex.org/keywords/pi","display_name":"Pi","score":0.7532628774642944},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.6638575196266174},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6235568523406982},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5148783922195435},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48077577352523804},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3422642648220062},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32700833678245544},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23625096678733826},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22935786843299866}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8220101594924927},{"id":"https://openalex.org/C53009064","wikidata":"https://www.wikidata.org/wiki/Q167","display_name":"Pi","level":2,"score":0.7532628774642944},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.6638575196266174},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6235568523406982},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5148783922195435},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48077577352523804},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3422642648220062},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32700833678245544},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23625096678733826},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22935786843299866}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-2015-02930-5","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2015-02930-5","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:HAL:hal-01174411v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01174411","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 2015, 84 (295), pp.2433 - 2446. &#x27E8;10.1090/S0025-5718-2015-02930-5#sthash.CxdZoPgC.dpuf&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/98757","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/98757","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation","raw_type":"Journal article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W146905023","https://openalex.org/W602889229","https://openalex.org/W1488906634","https://openalex.org/W1512503533","https://openalex.org/W1576065923","https://openalex.org/W1982457411","https://openalex.org/W2029369498","https://openalex.org/W2075274710","https://openalex.org/W2102814447","https://openalex.org/W2951055021","https://openalex.org/W2986262373"],"related_works":["https://openalex.org/W2030762054","https://openalex.org/W3157618815","https://openalex.org/W2401345448","https://openalex.org/W255820224","https://openalex.org/W2278807000","https://openalex.org/W2964228179","https://openalex.org/W2628590989","https://openalex.org/W2742629407","https://openalex.org/W279885097","https://openalex.org/W3137738104"],"abstract_inverted_index":{"We":[0],"consider":[1,76],"the":[2,101,117,128],"least":[3],"number":[4],"<inline-formula":[5,24,103],"content-type=\"math/mathml\">":[6,25,104],"<mml:math":[7,26,105],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[8,27,106],"alttext=\"x\">":[9,107],"<mml:semantics>":[10,40,108],"<mml:mi>x</mml:mi>":[11,47,62,109],"<mml:annotation":[12,66,110],"encoding=\"application/x-tex\">x</mml:annotation>":[13,111],"</mml:semantics>":[14,70,112],"</mml:math>":[15,71,113],"</inline-formula>":[16,72,114],"for":[17,100,115],"which":[18,116],"a":[19,95],"change":[20],"of":[21,23,78,88],"sign":[22],"alttext=\"pi":[28],"left-parenthesis":[29,37],"x":[30,38],"right-parenthesis":[31],"minus":[32],"normal":[33,35],"l":[34],"i":[36],"right-parenthesis\">":[39],"<mml:mrow>":[41],"<mml:mi>":[42],"\u03c0":[43],"</mml:mi>":[44],"<mml:mo":[45,48,60,63],"stretchy=\"false\">(</mml:mo>":[46,61],"stretchy=\"false\">)</mml:mo>":[49,64],"<mml:mo>":[50],"\u2212":[51],"</mml:mo>":[52],"<mml:mrow":[53],"class=\"MJX-TeXAtom-ORD\">":[54],"<mml:mi":[55,57],"mathvariant=\"normal\">l</mml:mi>":[56],"mathvariant=\"normal\">i</mml:mi>":[58],"</mml:mrow>":[59,65],"encoding=\"application/x-tex\">\\pi":[67],"(x)-\\mathrm":[68],"{li}(x)</mml:annotation>":[69],"occurs.":[73],"First,":[74],"we":[75,93,122],"modifications":[77],"Lehman\u2019s":[79],"method":[80],"that":[81],"enable":[82],"us":[83],"to":[84,126],"obtain":[85],"better":[86],"estimates":[87],"some":[89],"error":[90],"terms.":[91],"Second,":[92],"establish":[94],"new":[96],"smaller":[97],"upper":[98],"bound":[99],"first":[102],"difference":[118],"is":[119],"positive.":[120],"Third,":[121],"use":[123],"numerical":[124],"computations":[125],"improve":[127],"final":[129],"result.":[130]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}
