{"id":"https://openalex.org/W1539523659","doi":"https://doi.org/10.1090/mcom/3021","title":"On the first sign change of \ud835\udf03(\ud835\udc65)-\ud835\udc65","display_name":"On the first sign change of \ud835\udf03(\ud835\udc65)-\ud835\udc65","publication_year":2015,"publication_date":"2015-08-21","ids":{"openalex":"https://openalex.org/W1539523659","doi":"https://doi.org/10.1090/mcom/3021","mag":"1539523659"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3021","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3021","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":true,"oa_status":"green","oa_url":"https://research-information.bris.ac.uk/files/70486800/Skewestheta8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064602704","display_name":"David J. Platt","orcid":"https://orcid.org/0000-0003-1926-1465"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]},{"id":"https://openalex.org/I4210166532","display_name":"Heilbronn Institute for Mathematical Research","ror":"https://ror.org/05ttdgs63","country_code":"GB","type":"facility","lineage":["https://openalex.org/I4210166532"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"D. Platt","raw_affiliation_strings":["Heilbronn Institute for Mathematical Research University of Bristol, Bristol, United Kingdom","School of Mathematics"],"affiliations":[{"raw_affiliation_string":"Heilbronn Institute for Mathematical Research University of Bristol, Bristol, United Kingdom","institution_ids":["https://openalex.org/I4210166532","https://openalex.org/I36234482"]},{"raw_affiliation_string":"School of Mathematics","institution_ids":[]}]},{"author_position":"last","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":"T. Trudgian","raw_affiliation_strings":["Mathematical Sciences Institute, The Australian National University, ACT 0200, Australia","Australian Natl Univ"],"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Institute, The Australian National University, ACT 0200, Australia","institution_ids":["https://openalex.org/I2802631561","https://openalex.org/I118347636"]},{"raw_affiliation_string":"Australian Natl Univ","institution_ids":["https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064602704"],"corresponding_institution_ids":["https://openalex.org/I36234482","https://openalex.org/I4210166532"],"apc_list":null,"apc_paid":null,"fwci":8.74,"has_fulltext":true,"cited_by_count":63,"citation_normalized_percentile":{"value":0.98369565,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"85","issue":"299","first_page":"1539","last_page":"1547"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9993000030517578,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.994700014591217,"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/mathematics","display_name":"Mathematics","score":0.8167732954025269},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.7316989898681641},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5565085411071777},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2729603946208954}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8167732954025269},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.7316989898681641},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5565085411071777},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2729603946208954}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/mcom/3021","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3021","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:research-information.bris.ac.uk:publications/ef81d376-24d3-40b5-a064-d1b8f630d199","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/ef81d376-24d3-40b5-a064-d1b8f630d199","pdf_url":"https://research-information.bris.ac.uk/files/70486800/Skewestheta8.pdf","source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Platt, D J & Trudgian, T 2015, 'On the first sign change of \u03b8(x) - x', Mathematics of Computation, vol. 85, pp. 1539-1547. https://doi.org/10.1090/mcom/3021","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/ef81d376-24d3-40b5-a064-d1b8f630d199","is_oa":false,"landing_page_url":"https://hdl.handle.net/1983/ef81d376-24d3-40b5-a064-d1b8f630d199","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:research-information.bris.ac.uk:publications/ef81d376-24d3-40b5-a064-d1b8f630d199","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/ef81d376-24d3-40b5-a064-d1b8f630d199","pdf_url":"https://research-information.bris.ac.uk/files/70486800/Skewestheta8.pdf","source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Platt, D J & Trudgian, T 2015, 'On the first sign change of \u03b8(x) - x', Mathematics of Computation, vol. 85, pp. 1539-1547. https://doi.org/10.1090/mcom/3021","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G386373909","display_name":null,"funder_award_id":"DE120100173","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1539523659.pdf","grobid_xml":"https://content.openalex.org/works/W1539523659.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W602889229","https://openalex.org/W744724794","https://openalex.org/W1480319329","https://openalex.org/W1507390359","https://openalex.org/W1512503533","https://openalex.org/W1530543069","https://openalex.org/W1552861997","https://openalex.org/W1567653974","https://openalex.org/W1576065923","https://openalex.org/W1675900842","https://openalex.org/W1978559180","https://openalex.org/W1982457411","https://openalex.org/W2018035394","https://openalex.org/W2102814447","https://openalex.org/W2107996047","https://openalex.org/W2316210826","https://openalex.org/W2331905370","https://openalex.org/W2594998506","https://openalex.org/W2617116203","https://openalex.org/W2906953798","https://openalex.org/W2986262373"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,64,94,140,172],"content-type=\"math/mathml\">":[2,65,95,141,173],"<mml:math":[3,66,96,142,174],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,67,97,143,175],"alttext=\"theta":[5,68,176],"left-parenthesis":[6,69,147,177],"x":[7,14,70,100,178,181],"right-parenthesis":[8,71,179],"equals":[9],"sigma-summation":[10],"Underscript":[11],"p":[12],"less-than-or-equal-to":[13],"Endscripts":[15],"log":[16],"p\">":[17],"<mml:semantics>":[18,74,107,150,183],"<mml:mrow>":[19,75,108,151,184],"<mml:mi>":[20,76,185],"\u03b8":[21,77,186],"</mml:mi>":[22,78,187],"<mml:mo":[23,26,79,82,158,161,188,191],"stretchy=\"false\">(</mml:mo>":[24,80,159,189],"<mml:mi>x</mml:mi>":[25,39,81,85,111,152,190,194],"stretchy=\"false\">)</mml:mo>":[27,83,162,192],"<mml:mo>=</mml:mo>":[28],"<mml:munder>":[29],"<mml:mo>":[30,36,43,114,155],"\u2211":[31],"</mml:mo>":[32,38,45,116,157],"<mml:mrow":[33,119],"class=\"MJX-TeXAtom-ORD\">":[34,120],"<mml:mi>p</mml:mi>":[35,46],"\u2264":[37],"</mml:mrow>":[40,47,86,122,124,163,196],"</mml:munder>":[41],"<mml:mi>log</mml:mi>":[42],"\u2061":[44,156],"<mml:annotation":[48,87,125,164,197],"encoding=\"application/x-tex\">\\theta":[49,88,198],"(x)":[50,199],"=":[51],"\\sum":[52],"_{p\\leq":[53],"x}":[54],"\\log":[55],"p</mml:annotation>":[56],"</mml:semantics>":[57,90,129,167,201],"</mml:math>":[58,91,130,168,202],"</inline-formula>":[59,92,131,169,203],".":[60,132],"We":[61,133],"show":[62,135],"that":[63,136],"greater-than":[72,99,101,145,180],"x\">":[73],"<mml:mo>&gt;</mml:mo>":[84,110,112,153,193],"(x)&gt;x</mml:annotation>":[89],"for":[93,170],"alttext=\"2":[98],"1.39":[102],"dot":[103],"10":[104],"Superscript":[105],"17\">":[106],"<mml:mn>2</mml:mn>":[109],"<mml:mn>1.39</mml:mn>":[113],"\u22c5":[115],"<mml:msup>":[117],"<mml:mn>10</mml:mn>":[118],"<mml:mn>17</mml:mn>":[121],"</mml:msup>":[123],"encoding=\"application/x-tex\">2&gt;x&gt;":[126],"1.39\\cdot":[127],"10^{17}</mml:annotation>":[128],"also":[134],"there":[137],"is":[138],"an":[139],"alttext=\"x":[144],"exp":[146],"727.951332668":[148],"right-parenthesis\">":[149],"<mml:mi>exp</mml:mi>":[154],"<mml:mn>727.951332668</mml:mn>":[160],"encoding=\"application/x-tex\">x&gt;\\exp":[165],"(727.951332668)</mml:annotation>":[166],"which":[171],"period\">":[182],"<mml:mo>.</mml:mo>":[195],"&gt;x.</mml:annotation>":[200]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2016-06-24T00:00:00"}
