{"id":"https://openalex.org/W2550792289","doi":"https://doi.org/10.1090/mcom/3328","title":"Faster integer multiplication using plain vanilla FFT primes","display_name":"Faster integer multiplication using plain vanilla FFT primes","publication_year":2017,"publication_date":"2017-10-18","ids":{"openalex":"https://openalex.org/W2550792289","doi":"https://doi.org/10.1090/mcom/3328","mag":"2550792289"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3328","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3328","pdf_url":"https://www.ams.org/mcom/2019-88-315/S0025-5718-2018-03328-2/S0025-5718-2018-03328-2.pdf","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":"bronze","oa_url":"https://www.ams.org/mcom/2019-88-315/S0025-5718-2018-03328-2/S0025-5718-2018-03328-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014621753","display_name":"David Harvey","orcid":"https://orcid.org/0000-0002-4933-658X"},"institutions":[{"id":"https://openalex.org/I3130638677","display_name":"Edinburgh College","ror":"https://ror.org/04vpa6h32","country_code":"GB","type":"education","lineage":["https://openalex.org/I3130638677"]},{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["AU","GB"],"is_corresponding":true,"raw_author_name":"David Harvey","raw_affiliation_strings":["School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia","Edin. - University of Edinburgh (Old College South Bridge Edinburgh EH8 9YL - United Kingdom)"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"Edin. - University of Edinburgh (Old College South Bridge Edinburgh EH8 9YL - United Kingdom)","institution_ids":["https://openalex.org/I3130638677","https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001033788","display_name":"Joris van der Hoeven","orcid":"https://orcid.org/0000-0003-2244-1897"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Joris van der Hoeven","raw_affiliation_strings":["CNRS, Laboratoire d\u00e2\u0080\u0099informatique, UMR 7161 CNRS, \u00c3\u0089cole polytechnique, 91128 Palaiseau, France","LIX - Laboratoire d'informatique de l'\u00c9cole polytechnique [Palaiseau] (1 Rue Honor\u00e9 d\u2019Estienne d\u2019Orves, B\u00e2timent Alain Turing, 91120 Palaiseau - France)"],"affiliations":[{"raw_affiliation_string":"CNRS, Laboratoire d\u00e2\u0080\u0099informatique, UMR 7161 CNRS, \u00c3\u0089cole polytechnique, 91128 Palaiseau, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LIX - Laboratoire d'informatique de l'\u00c9cole polytechnique [Palaiseau] (1 Rue Honor\u00e9 d\u2019Estienne d\u2019Orves, B\u00e2timent Alain Turing, 91120 Palaiseau - France)","institution_ids":["https://openalex.org/I4210139461","https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014621753"],"corresponding_institution_ids":["https://openalex.org/I3130638677","https://openalex.org/I31746571","https://openalex.org/I98677209"],"apc_list":null,"apc_paid":null,"fwci":3.0354,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.92530397,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"88","issue":"315","first_page":"501","last_page":"514"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9977999925613403,"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":0.8945621848106384},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.7337366342544556},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6376887559890747},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6291173100471497},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.6149591207504272},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6000993251800537},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4959014356136322},{"id":"https://openalex.org/keywords/arithmetic-progression","display_name":"Arithmetic progression","score":0.49064627289772034},{"id":"https://openalex.org/keywords/prime-factor","display_name":"Prime factor","score":0.4857076108455658},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40254417061805725},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39305076003074646},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14722555875778198},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07339110970497131},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05373257398605347}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8945621848106384},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7337366342544556},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6376887559890747},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6291173100471497},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.6149591207504272},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6000993251800537},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4959014356136322},{"id":"https://openalex.org/C130498168","wikidata":"https://www.wikidata.org/wiki/Q170008","display_name":"Arithmetic progression","level":2,"score":0.49064627289772034},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.4857076108455658},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40254417061805725},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39305076003074646},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14722555875778198},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07339110970497131},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05373257398605347},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/3328","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3328","pdf_url":"https://www.ams.org/mcom/2019-88-315/S0025-5718-2018-03328-2/S0025-5718-2018-03328-2.pdf","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:1611.07144","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.07144","pdf_url":"https://arxiv.org/pdf/1611.07144","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-02350423v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02350423","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, 2019, 88 (315), pp.501-514. &#x27E8;10.1090/mcom/3328&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:unsworks.library.unsw.edu.au:1959.4/105114","is_oa":false,"landing_page_url":"http://hdl.handle.net/1959.4/105114","pdf_url":null,"source":{"id":"https://openalex.org/S4306401737","display_name":"UNSWorks (University of New South Wales, Sydney, Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40053085","host_organization_name":"Australian Defence Force Academy","host_organization_lineage":["https://openalex.org/I40053085"],"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, 88, 315, 501-514","raw_type":"http://purl.org/coar/resource_type/c_6501"}],"best_oa_location":{"id":"doi:10.1090/mcom/3328","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3328","pdf_url":"https://www.ams.org/mcom/2019-88-315/S0025-5718-2018-03328-2/S0025-5718-2018-03328-2.pdf","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4774827301","display_name":null,"funder_award_id":"DP150101689","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G5870524844","display_name":null,"funder_award_id":"FT160100219","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/W2550792289.pdf","grobid_xml":"https://content.openalex.org/works/W2550792289.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1562183207","https://openalex.org/W1754110195","https://openalex.org/W1964626890","https://openalex.org/W2020142281","https://openalex.org/W2029536980","https://openalex.org/W2034013822","https://openalex.org/W2045826589","https://openalex.org/W2061171222","https://openalex.org/W2067507719","https://openalex.org/W2069448237","https://openalex.org/W2078645706","https://openalex.org/W2083368929","https://openalex.org/W2084801848","https://openalex.org/W2087957223","https://openalex.org/W2102045564","https://openalex.org/W2156734628","https://openalex.org/W2159341052","https://openalex.org/W2322416844","https://openalex.org/W2962979000","https://openalex.org/W2963464756","https://openalex.org/W6742592995","https://openalex.org/W6831028937"],"related_works":["https://openalex.org/W3046688035","https://openalex.org/W2012363129","https://openalex.org/W2375604274","https://openalex.org/W29235628","https://openalex.org/W4287997543","https://openalex.org/W2036352952","https://openalex.org/W2066431770","https://openalex.org/W2321841381","https://openalex.org/W4289785671","https://openalex.org/W1514060060"],"abstract_inverted_index":{"Assuming":[0],"a":[1],"conjectural":[2],"upper":[3],"bound":[4],"for":[5],"the":[6],"least":[7],"prime":[8],"in":[9,33],"an":[10],"arithmetic":[11],"progression,":[12],"we":[13],"show":[14],"that":[15],"<inline-formula":[16,34],"content-type=\"math/mathml\">":[17,35],"<mml:math":[18,36],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[19,37],"alttext=\"n\">":[20],"<mml:semantics>":[21,54],"<mml:mi>n</mml:mi>":[22,59,64,80],"<mml:annotation":[23,86],"encoding=\"application/x-tex\">n</mml:annotation>":[24],"</mml:semantics>":[25,93],"</mml:math>":[26,94],"</inline-formula>":[27,95],"-bit":[28],"integers":[29],"may":[30],"be":[31],"multiplied":[32],"alttext=\"upper":[38],"O":[39],"left-parenthesis":[40],"n":[41,43,51],"log":[42,46],"4":[44],"Superscript":[45,48,50],"Super":[47],"asterisk":[49],"Baseline":[52],"right-parenthesis\">":[53],"<mml:mrow>":[55],"<mml:mi>O</mml:mi>":[56],"<mml:mo":[57,83],"stretchy=\"false\">(</mml:mo>":[58],"<mml:mi>log</mml:mi>":[60,72],"<mml:mo>":[61,73,77],"\u2061":[62,78],"</mml:mo>":[63,75,79],"<mml:mspace":[65],"width=\"thinmathspace\"/>":[66],"<mml:msup>":[67,71],"<mml:mn>4</mml:mn>":[68],"<mml:mrow":[69],"class=\"MJX-TeXAtom-ORD\">":[70],"\u2217":[74],"</mml:msup>":[76,82],"</mml:mrow>":[81,85],"stretchy=\"false\">)</mml:mo>":[84],"encoding=\"application/x-tex\">O(n":[87],"\\log":[88],"n\\,":[89],"4^{\\log":[90],"^*":[91],"n})</mml:annotation>":[92],"bit":[96],"operations.":[97]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}
