{"id":"https://openalex.org/W2402427945","doi":"https://doi.org/10.4169/amer.math.monthly.119.08.690","title":"Evaluation of Certain Legendre Symbols","display_name":"Evaluation of Certain Legendre Symbols","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2402427945","doi":"https://doi.org/10.4169/amer.math.monthly.119.08.690","mag":"2402427945"},"language":"en","primary_location":{"id":"doi:10.4169/amer.math.monthly.119.08.690","is_oa":false,"landing_page_url":"https://doi.org/10.4169/amer.math.monthly.119.08.690","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012715334","display_name":"David Angell","orcid":"https://orcid.org/0000-0002-1203-684X"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"David Angell","raw_affiliation_strings":["School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia david.angell@unsw.edu.au"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia david.angell@unsw.edu.au","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5012715334"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":null,"apc_paid":null,"fwci":0.2425,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.59768293,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"119","issue":"8","first_page":"690","last_page":"690"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.6330999732017517,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.6330999732017517,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.605400025844574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/legendre-symbol","display_name":"Legendre symbol","score":0.9393190145492554},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.8877213001251221},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.7043571472167969},{"id":"https://openalex.org/keywords/symbol","display_name":"Symbol (formal)","score":0.6424695253372192},{"id":"https://openalex.org/keywords/associated-legendre-polynomials","display_name":"Associated Legendre polynomials","score":0.6215952038764954},{"id":"https://openalex.org/keywords/legendres-equation","display_name":"Legendre's equation","score":0.5477504134178162},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5304740071296692},{"id":"https://openalex.org/keywords/legendre-function","display_name":"Legendre function","score":0.48192524909973145},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.41468796133995056},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30243372917175293},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18967464566230774},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.17224064469337463},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1598602533340454},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14818075299263},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.11757728457450867},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08610716462135315}],"concepts":[{"id":"https://openalex.org/C165656649","wikidata":"https://www.wikidata.org/wiki/Q748339","display_name":"Legendre symbol","level":5,"score":0.9393190145492554},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.8877213001251221},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.7043571472167969},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.6424695253372192},{"id":"https://openalex.org/C36956377","wikidata":"https://www.wikidata.org/wiki/Q228376","display_name":"Associated Legendre polynomials","level":5,"score":0.6215952038764954},{"id":"https://openalex.org/C86287605","wikidata":"https://www.wikidata.org/wiki/Q4454970","display_name":"Legendre's equation","level":3,"score":0.5477504134178162},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5304740071296692},{"id":"https://openalex.org/C153262748","wikidata":"https://www.wikidata.org/wiki/Q17098449","display_name":"Legendre function","level":3,"score":0.48192524909973145},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.41468796133995056},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30243372917175293},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18967464566230774},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.17224064469337463},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1598602533340454},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14818075299263},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.11757728457450867},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08610716462135315},{"id":"https://openalex.org/C95136341","wikidata":"https://www.wikidata.org/wiki/Q625519","display_name":"Quadratic field","level":4,"score":0.0},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.0},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.0},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.0},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4169/amer.math.monthly.119.08.690","is_oa":false,"landing_page_url":"https://doi.org/10.4169/amer.math.monthly.119.08.690","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1607269076","https://openalex.org/W2953361964","https://openalex.org/W2021432593","https://openalex.org/W1988418937","https://openalex.org/W3005861762","https://openalex.org/W3200178185","https://openalex.org/W2053826141","https://openalex.org/W3130427480","https://openalex.org/W2402427945","https://openalex.org/W4299530270"],"abstract_inverted_index":{"We":[0],"state":[1],"and":[2,20],"prove":[3],"an":[4],"apparently":[5],"hitherto":[6],"unrecorded":[7],"evaluation":[8],"of":[9],"certain":[10],"Legendre":[11,28],"symbols:":[12],"if":[13],"p":[14,17,23],"is":[15,30],"prime,":[16],"\u2260":[18],"2,":[19],"ab":[21],"=":[22],"\u2212":[24],"1,":[25],"then":[26],"the":[27],"symbol":[29],"given":[31],"by":[32]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}