{"id":"https://openalex.org/W3207837863","doi":"https://doi.org/10.1090/mcom/3848","title":"Divisibility conditions on the order of the reductions of algebraic numbers","display_name":"Divisibility conditions on the order of the reductions of algebraic numbers","publication_year":2023,"publication_date":"2023-03-29","ids":{"openalex":"https://openalex.org/W3207837863","doi":"https://doi.org/10.1090/mcom/3848","mag":"3207837863"},"language":"fi","primary_location":{"id":"doi:10.1090/mcom/3848","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1090/mcom/3848","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":"http://arxiv.org/abs/2110.08911","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028240383","display_name":"Pietro Sgobba","orcid":"https://orcid.org/0000-0001-5434-0308"},"institutions":[{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]}],"countries":["LU"],"is_corresponding":true,"raw_author_name":"Pietro Sgobba","raw_affiliation_strings":["Department of Mathematics, University of Luxembourg, 6 Avenue de la Fonte, 4364 Esch-sur-Alzette, Luxembourg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Luxembourg, 6 Avenue de la Fonte, 4364 Esch-sur-Alzette, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028240383"],"corresponding_institution_ids":["https://openalex.org/I186903577"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02852776,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"92","issue":"343","first_page":"2281","last_page":"2305"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9997000098228455,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9997000098228455,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9961000084877014,"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/algorithm","display_name":"Algorithm","score":0.6806191205978394},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.5688071846961975},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.417807936668396},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.36448216438293457},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36123645305633545}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6806191205978394},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.5688071846961975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.417807936668396},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36448216438293457},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36123645305633545}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3848","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1090/mcom/3848","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:orbilu.uni.lu:10993/46613","is_oa":true,"landing_page_url":"http://orbilu.uni.lu/handle/10993/46613","pdf_url":"http://arxiv.org/abs/2110.08911","source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"working paper"}],"best_oa_location":{"id":"pmh:oai:orbilu.uni.lu:10993/46613","is_oa":true,"landing_page_url":"http://orbilu.uni.lu/handle/10993/46613","pdf_url":"http://arxiv.org/abs/2110.08911","source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"working paper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3207837863.pdf","grobid_xml":"https://content.openalex.org/works/W3207837863.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1480319329","https://openalex.org/W1480788671","https://openalex.org/W1501162952","https://openalex.org/W1967677714","https://openalex.org/W1975664169","https://openalex.org/W1992416585","https://openalex.org/W2001183595","https://openalex.org/W2064771743","https://openalex.org/W2078351417","https://openalex.org/W2155898253","https://openalex.org/W2335187233","https://openalex.org/W2344907887","https://openalex.org/W2402967980","https://openalex.org/W2789681260","https://openalex.org/W2892812739","https://openalex.org/W2894975758","https://openalex.org/W2937903557","https://openalex.org/W2963115395","https://openalex.org/W3045788473","https://openalex.org/W3088807789","https://openalex.org/W3100388377","https://openalex.org/W3106010426","https://openalex.org/W4256128629","https://openalex.org/W4287960381","https://openalex.org/W4313422331","https://openalex.org/W6682947522","https://openalex.org/W6754974678"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W2392921965","https://openalex.org/W2358755282","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,20,39,77,96,114,172,195,217,238,263],"content-type=\"math/mathml\">":[2,21,40,78,97,115,173,196,218,239,264],"<mml:math":[3,22,41,79,98,116,174,197,219,240,265],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,23,42,80,99,117,175,198,220,241,266],"alttext=\"upper":[5,24,43,100],"K\">":[6,101],"<mml:semantics>":[7,26,47,83,102,125,178,200,223,244,269],"<mml:mi>K</mml:mi>":[8,49,103],"<mml:annotation":[9,28,54,89,104,141,184,202,227,248,275],"encoding=\"application/x-tex\">K</mml:annotation>":[10,105],"</mml:semantics>":[11,30,56,92,106,145,187,204,229,250,278],"</mml:math>":[12,31,57,93,107,146,188,205,230,251,279],"</inline-formula>":[13,32,58,94,108,147,189,206,231,252,280],"be":[14,33,282],"a":[15,34,151,157,215],"number":[16,74,304],"field,":[17],"and":[18,208],"let":[19],"G\">":[25],"<mml:mi>G</mml:mi>":[27,129],"encoding=\"application/x-tex\">G</mml:annotation>":[29],"finitely":[35,235],"generated":[36],"subgroup":[37],"of":[38,75,95,113,164,262,295,303],"K":[44],"Superscript":[45],"times\">":[46],"<mml:msup>":[48],"<mml:mo>":[50],"\u00d7":[51],"</mml:mo>":[52],"</mml:msup>":[53],"encoding=\"application/x-tex\">K^\\times</mml:annotation>":[55],".":[59,253],"Without":[60],"relying":[61],"on":[62,257],"the":[63,73,111,161,170,192,212,258,296],"Generalized":[64],"Riemann":[65],"Hypothesis":[66],"we":[67,168,290],"prove":[68,291],"an":[69,292],"asymptotic":[70],"formula":[71],"for":[72,160,190,210,234,300],"primes":[76,171,237],"alttext=\"German":[81,176,267],"p\">":[82,177,268],"<mml:mrow":[84,133,179,270],"class=\"MJX-TeXAtom-ORD\">":[85,134,180,271],"<mml:mi":[86,135,181,272],"mathvariant=\"fraktur\">p</mml:mi>":[87,136,182,273],"</mml:mrow>":[88,137,140,183,274],"encoding=\"application/x-tex\">\\mathfrak":[90,185,276],"p</mml:annotation>":[91,186,277],"such":[109],"that":[110],"order":[112,193,213,285],"alttext=\"left-parenthesis":[118],"upper":[119],"G":[120],"mod":[121],"German":[122],"p":[123],"right-parenthesis\">":[124],"<mml:mrow>":[126],"<mml:mo":[127,130,138],"stretchy=\"false\">(</mml:mo>":[128],"lspace=\"thickmathspace\"":[131],"rspace=\"thickmathspace\">mod</mml:mo>":[132],"stretchy=\"false\">)</mml:mo>":[139],"encoding=\"application/x-tex\">(G\\bmod":[142],"\\mathfrak":[143],"p)</mml:annotation>":[144],"is":[148,194],"divisible":[149],"by":[150],"fixed":[152],"integer.":[153],"We":[154],"also":[155],"provide":[156],"rational":[158],"expression":[159],"natural":[162],"density":[163,298],"this":[165],"set.":[166],"Furthermore,":[167],"study":[169],"which":[191,211],"alttext=\"k\">":[199],"<mml:mi>k</mml:mi>":[201],"encoding=\"application/x-tex\">k</mml:annotation>":[203],"-free,":[207],"those":[209],"has":[214],"prescribed":[216],"alttext=\"script":[221,242],"l\">":[222,243],"<mml:mi>":[224,245],"\u2113":[225,246],"</mml:mi>":[226,247],"encoding=\"application/x-tex\">\\ell</mml:annotation>":[228,249],"-adic":[232],"valuation":[233],"many":[236],"An":[254],"additional":[255],"condition":[256],"Frobenius":[259],"conjugacy":[260],"class":[261],"may":[281],"considered.":[283],"In":[284],"to":[286],"establish":[287],"these":[288],"results,":[289],"unconditional":[293],"version":[294],"Chebotarev":[297],"theorem":[299],"Kummer":[301],"extensions":[302],"fields.":[305]},"counts_by_year":[],"updated_date":"2026-04-23T06:14:38.165362","created_date":"2025-10-10T00:00:00"}
