{"id":"https://openalex.org/W2057890541","doi":"https://doi.org/10.1090/s0025-5718-01-01382-5","title":"Numerical calculation of the density of prime numbers with a given least primitive root","display_name":"Numerical calculation of the density of prime numbers with a given least primitive root","publication_year":2001,"publication_date":"2001-11-28","ids":{"openalex":"https://openalex.org/W2057890541","doi":"https://doi.org/10.1090/s0025-5718-01-01382-5","mag":"2057890541"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01382-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01382-5","pdf_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01382-5/S0025-5718-01-01382-5.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":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01382-5/S0025-5718-01-01382-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075897693","display_name":"Andrzej Paszkiewicz","orcid":"https://orcid.org/0000-0001-7573-3856"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"A. Paszkiewicz","raw_affiliation_strings":["Warsaw University of Technology, Institute of Telecommunications, Division of Telecommunications Fundamental, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Warsaw University of Technology, Institute of Telecommunications, Division of Telecommunications Fundamental, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland","institution_ids":["https://openalex.org/I108403487"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010455224","display_name":"Andrzej Schinzel","orcid":null},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"A. Schinzel","raw_affiliation_strings":["Institute of Mathematics, Polish Academy of Sciences, ul. \u00c5\u009aniadeckich 8, 00-950 Warsaw, Poland","Institute of Mathematics, Polish Academy of Sciences, ul.Sniadeckich 8, 00-950 Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Polish Academy of Sciences, ul. \u00c5\u009aniadeckich 8, 00-950 Warsaw, Poland","institution_ids":["https://openalex.org/I99542240","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Institute of Mathematics, Polish Academy of Sciences, ul.Sniadeckich 8, 00-950 Warsaw, Poland","institution_ids":["https://openalex.org/I99542240","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5075897693"],"corresponding_institution_ids":["https://openalex.org/I108403487"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.20762053,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"71","issue":"240","first_page":"1781","last_page":"1797"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9587000012397766,"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":0.9587000012397766,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9330000281333923,"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":0.9192761182785034},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.5665551424026489},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4768306314945221},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2758873403072357}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9192761182785034},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.5665551424026489},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4768306314945221},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2758873403072357},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-01-01382-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01382-5","pdf_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01382-5/S0025-5718-01-01382-5.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"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01382-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01382-5","pdf_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01382-5/S0025-5718-01-01382-5.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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2057890541.pdf","grobid_xml":"https://content.openalex.org/works/W2057890541.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W956517583","https://openalex.org/W1125383745","https://openalex.org/W2061619918","https://openalex.org/W2129477538"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W4238204885"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"the":[3,44,93,110,113,125],"densities":[4],"<inline-formula":[5,31,48,76],"content-type=\"math/mathml\">":[6,32,49,77],"<mml:math":[7,33,50,78],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[8,34,51,79],"alttext=\"upper":[9],"D":[10],"left-parenthesis":[11,53],"i":[12],"right-parenthesis\">":[13],"<mml:semantics>":[14,36,58,81],"<mml:mrow>":[15,59],"<mml:mi>D</mml:mi>":[16],"<mml:mo":[17,20,61,64],"stretchy=\"false\">(</mml:mo>":[18,62],"<mml:mi>i</mml:mi>":[19,67,82],"stretchy=\"false\">)</mml:mo>":[21,65],"</mml:mrow>":[22,68],"<mml:annotation":[23,38,69,83],"encoding=\"application/x-tex\">D(i)</mml:annotation>":[24],"</mml:semantics>":[25,40,71,85],"</mml:math>":[26,41,72,86],"</inline-formula>":[27,42,73,87],"of":[28,92,112,119,127],"prime":[29],"numbers":[30],"alttext=\"p\">":[35],"<mml:mi>p</mml:mi>":[37,63],"encoding=\"application/x-tex\">p</mml:annotation>":[39],"having":[43],"least":[45],"primitive":[46],"root":[47],"alttext=\"g":[52],"p":[54],"right-parenthesis":[55],"equals":[56],"i\">":[57],"<mml:mi>g</mml:mi>":[60],"<mml:mo>=</mml:mo>":[66],"encoding=\"application/x-tex\">g(p)=i</mml:annotation>":[70],",":[74],"where":[75],"alttext=\"i\">":[80],"encoding=\"application/x-tex\">i</mml:annotation>":[84],"is":[88],"equal":[89],"to":[90],"one":[91],"initial":[94],"positive":[95],"integers":[96],"less":[97],"than":[98],"32,":[99],"have":[100],"been":[101],"numerically":[102],"calculated.":[103],"The":[104,117],"computations":[105,121],"were":[106,122],"carried":[107],"out":[108],"under":[109],"assumption":[111],"Generalised":[114],"Riemann":[115],"Hypothesis.":[116],"results":[118,126],"these":[120],"compared":[123],"with":[124],"numerical":[128],"frequency":[129],"estimations.":[130]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
