{"id":"https://openalex.org/W2611472186","doi":"https://doi.org/10.4086/toc.2011.v007a009","title":"","display_name":"","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2611472186","doi":"https://doi.org/10.4086/toc.2011.v007a009","mag":"2611472186"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2011.v007a009","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2011.v007a009","pdf_url":"https://theoryofcomputing.org/articles/v007a009/v007a009.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v007a009/v007a009.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044999305","display_name":"Shachar Lovett","orcid":"https://orcid.org/0000-0003-4552-1443"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shachar Lovett","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059452045","display_name":"Roy Meshulam","orcid":"https://orcid.org/0000-0003-3804-4300"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roy Meshulam","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004360801","display_name":"Alex Samorodnitsky","orcid":"https://orcid.org/0000-0001-8643-7948"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alex Samorodnitsky","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044999305"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2752,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.94929779,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"7","issue":"1","first_page":"131","last_page":"145"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9846000075340271,"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":0.9846000075340271,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.970300018787384,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9688000082969666,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7766633033752441},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7756178975105286},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.762003481388092},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5675036311149597},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5582216382026672},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5271634459495544},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4958990514278412},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4503423869609833},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4493164122104645},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4429386258125305},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3921542763710022},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07702398300170898},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07423576712608337}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7766633033752441},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7756178975105286},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.762003481388092},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5675036311149597},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5582216382026672},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5271634459495544},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4958990514278412},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4503423869609833},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4493164122104645},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4429386258125305},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3921542763710022},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07702398300170898},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07423576712608337},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2011.v007a009","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2011.v007a009","pdf_url":"https://theoryofcomputing.org/articles/v007a009/v007a009.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2011.v007a009","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2011.v007a009","pdf_url":"https://theoryofcomputing.org/articles/v007a009/v007a009.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2611472186.pdf","grobid_xml":"https://content.openalex.org/works/W2611472186.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1554682571","https://openalex.org/W1606480398","https://openalex.org/W2032359312","https://openalex.org/W2034946612","https://openalex.org/W2064334110","https://openalex.org/W2080132708","https://openalex.org/W2111478028","https://openalex.org/W2146466938","https://openalex.org/W2157443379","https://openalex.org/W2335400162","https://openalex.org/W2963585281","https://openalex.org/W3102618960","https://openalex.org/W3124591719","https://openalex.org/W3151527484"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W4297950433","https://openalex.org/W4287023968","https://openalex.org/W4288279572","https://openalex.org/W1973978937","https://openalex.org/W4286909116","https://openalex.org/W2982781090"],"abstract_inverted_index":{"Let":[0],"p":[1,34,36,85],"be":[2,9,82],"a":[3,10,28,43,54],"fixed":[4],"prime":[5,72],"number":[6],"and":[7,69,88],"N":[8,33],"large":[11],"integer.":[12],"The":[13,58],"\"Inverse":[14],"Conjecture":[15],"for":[16,64,70,84],"the":[17,23,79,116],"Gowers":[18,25,99],"norm\"":[19,26],"states":[20],"that":[21,39],"if":[22],"\"d-th":[24],"of":[27,46,109],"function":[29,96],"f":[30,49],":":[31],"F":[32,35],"is":[37,50,60,101,112],"non-negligible,":[38,102],"is,":[40],"larger":[41],"than":[42],"constant":[44],"independent":[45],"N,":[47],"then":[48],"non-trivially":[51],"correlated":[52],"to":[53,62,81,106],"degree-(d":[55],"-1)":[56],"polynomial.":[57],"conjecture":[59,80],"known":[61],"hold":[63],"d":[65,89],"=":[66,86,90],"2,":[67],"3":[68,111],"any":[71,107],"p.":[73],"In":[74],"this":[75],"paper":[76],"we":[77],"show":[78],"false":[83],"2":[87],"4,":[91],"by":[92,126],"presenting":[93],"an":[94],"explicit":[95],"whose":[97,104],"4-th":[98],"norm":[100],"but":[103],"correlation":[105,121],"polynomial":[108],"degree":[110],"exponentially":[113],"small.":[114],"Essentially":[115],"same":[117],"result":[118],"(with":[119],"different":[120],"bounds)":[122],"was":[123],"independently":[124],"obtained":[125]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T08:04:53.788161","created_date":"2017-05-12T00:00:00"}
