{"id":"https://openalex.org/W2050813462","doi":"https://doi.org/10.1090/s0025-5718-01-01312-6","title":"Jacobi sums and new families of irreducible polynomials of Gaussian periods","display_name":"Jacobi sums and new families of irreducible polynomials of Gaussian periods","publication_year":2001,"publication_date":"2001-05-11","ids":{"openalex":"https://openalex.org/W2050813462","doi":"https://doi.org/10.1090/s0025-5718-01-01312-6","mag":"2050813462"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-01-01312-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01312-6","pdf_url":"https://www.ams.org/mcom/2001-70-236/S0025-5718-01-01312-6/S0025-5718-01-01312-6.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/2001-70-236/S0025-5718-01-01312-6/S0025-5718-01-01312-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090697087","display_name":"F. Thaine","orcid":null},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"F. Thaine","raw_affiliation_strings":["Department of Mathematics and Statistics - CICMA, Concordia University, 1455, de Maisonneuve Blvd. W., Montreal, Quebec, H3G 1M8, Canada","Department of Mathematics and Statistics\u2013CICMA, Concordia University, 1455, de Maisonneuve Blvd. W., Montreal, Quebec, H3G 1M8, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics - CICMA, Concordia University, 1455, de Maisonneuve Blvd. W., Montreal, Quebec, H3G 1M8, Canada","institution_ids":["https://openalex.org/I60158472"]},{"raw_affiliation_string":"Department of Mathematics and Statistics\u2013CICMA, Concordia University, 1455, de Maisonneuve Blvd. W., Montreal, Quebec, H3G 1M8, Canada","institution_ids":["https://openalex.org/I60158472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090697087"],"corresponding_institution_ids":["https://openalex.org/I60158472"],"apc_list":null,"apc_paid":null,"fwci":1.4698,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.79177162,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"70","issue":"236","first_page":"1617","last_page":"1640"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9853000044822693,"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"}},"topics":[{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9853000044822693,"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"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9805999994277954,"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/T11130","display_name":"Coding theory and cryptography","score":0.9768000245094299,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6628752946853638},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.49941325187683105},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4466262459754944},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.43611353635787964}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6628752946853638},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.49941325187683105},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4466262459754944},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.43611353635787964}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-01-01312-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01312-6","pdf_url":"https://www.ams.org/mcom/2001-70-236/S0025-5718-01-01312-6/S0025-5718-01-01312-6.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:CiteSeerX.psu:10.1.1.192.3964","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.3964","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2001-70-236/S0025-5718-01-01312-6/S0025-5718-01-01312-6.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01312-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01312-6","pdf_url":"https://www.ams.org/mcom/2001-70-236/S0025-5718-01-01312-6/S0025-5718-01-01312-6.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":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.4300000071525574}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2050813462.pdf","grobid_xml":"https://content.openalex.org/works/W2050813462.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1512374421","https://openalex.org/W1515541504","https://openalex.org/W1537396177","https://openalex.org/W1558606648","https://openalex.org/W1566526104","https://openalex.org/W1584934214","https://openalex.org/W1967163105","https://openalex.org/W1977852626","https://openalex.org/W1997994143","https://openalex.org/W2000286442","https://openalex.org/W2021335688","https://openalex.org/W2029195947","https://openalex.org/W2039540157","https://openalex.org/W2099197486","https://openalex.org/W2327162874","https://openalex.org/W2327935394","https://openalex.org/W3043060850","https://openalex.org/W4235161648","https://openalex.org/W4254229644","https://openalex.org/W4292101538"],"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/W2625833328","https://openalex.org/W1533177136","https://openalex.org/W4380994516"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,20,39,55,75,94,124,137,190,322,356,395,446,491,523,556],"content-type=\"math/mathml\">":[2,21,40,56,76,95,125,138,191,323,357,396,447,492,524,557],"<mml:math":[3,22,41,57,77,96,126,139,192,324,358,397,448,493,525,558],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,23,42,58,78,97,127,140,193,325,359,398,449,494,526,559],"alttext=\"m":[5],"greater-than":[6],"2\">":[7],"<mml:semantics>":[8,27,44,62,81,103,129,155,238,335,367,412,451,503,532],"<mml:mrow>":[9,63,82,104,156,239,336,368,413,504,533],"<mml:mi>m</mml:mi>":[10,30,45,84,178,268,343],"<mml:mo>&gt;</mml:mo>":[11],"<mml:mn>2</mml:mn>":[12,83,257],"</mml:mrow>":[13,67,85,112,114,164,177,179,247,258,264,281,297,306,308,346,374,381,425,432,436,510,517,541,542],"<mml:annotation":[14,32,46,68,86,115,131,180,309,347,382,437,453,518,543],"encoding=\"application/x-tex\">m&gt;":[15],"2</mml:annotation>":[16],"</mml:semantics>":[17,35,48,71,88,117,133,182,319,352,385,442,455,520,547],"</mml:math>":[18,36,49,72,89,118,134,183,320,353,386,443,456,521,548],"</inline-formula>,":[19,321,354,522,549],"alttext=\"zeta":[24],"Subscript":[25,101,144,196,214,220,230,361,403,497,561,576],"m\">":[26,80,154],"<mml:msub>":[28,107,159,240,276,292,369,420,505],"<mml:mi>\u03b6</mml:mi>":[29,267],"</mml:msub>":[31,113,165,248,282,298,375,426,511],"encoding=\"application/x-tex\">\\zeta":[33],"_m</mml:annotation>":[34],"</inline-formula>":[37,73,90,119,135,387,444],"an":[38],"alttext=\"m\">":[43],"encoding=\"application/x-tex\">m</mml:annotation>":[47],"</inline-formula>-th":[50],"primitive":[51,121],"root":[52,122],"of":[53,462,550,553],"1,":[54],"alttext=\"q":[59,527],"identical-to":[60,410],"1\">":[61,334],"<mml:mi>q</mml:mi>":[64,111,130,163,169,261,452,509,534],"<mml:mo>\u2261</mml:mo>":[65,434],"<mml:mn>1</mml:mn>":[66,171,263,301,345],"encoding=\"application/x-tex\">q\\equiv":[69],"1</mml:annotation>":[70],"mod":[74,445],"alttext=\"2":[79],"encoding=\"application/x-tex\">2m</mml:annotation>":[87],"a":[91,120,197,217,328,460,473],"prime":[92],"number,":[93],"alttext=\"s":[98,399],"equals":[99,142,147,201,206,564,568],"s":[100,221,231,362,404,579],"q\">":[102],"<mml:mi>s</mml:mi>":[105,108,280,296,373,415,424],"<mml:mo>=</mml:mo>":[106,158,166,249,256],"<mml:mrow":[109,161,174,242,253,259,269,278,294,371,416,422,507,536],"class=\"MJX-TeXAtom-ORD\">":[110,162,175,243,254,260,270,279,295,372,417,423,508,537],"encoding=\"application/x-tex\">s=s_{q}</mml:annotation>":[116],"modulo":[123],"alttext=\"q\">":[128,450],"encoding=\"application/x-tex\">q</mml:annotation>":[132,454],"and":[136,472],"alttext=\"f":[141],"f":[143,571],"q":[145,149,209,498,577],"Baseline":[146,200,363,409,499,563],"left-parenthesis":[148,223,233,364,406,500],"minus":[150,202,210,235,333,572],"1":[151,211,234,573],"right-parenthesis":[152,225,408],"slash":[153],"<mml:mi>f</mml:mi>":[157,160],"<mml:mo":[167,172,283,286,299,304,376,379,427,430,512,515],"stretchy=\"false\">(</mml:mo>":[168,284,300,377,428,513],"<mml:mo>\u2212</mml:mo>":[170,250,262,302,344],"stretchy=\"false\">)</mml:mo>":[173,287,305,380,431,516],"<mml:mo>/</mml:mo>":[176],"encoding=\"application/x-tex\">f=f_{q}=(q-1)/m</mml:annotation>":[181],"</inline-formula>.":[184,457],"We":[185,458],"study":[186],"the":[187,389],"Jacobi":[188],"sums":[189],"alttext=\"upper":[194,495],"J":[195],"comma":[198,329],"b":[199,227,330],"sigma-summation":[203,565],"Underscript":[204,566],"k":[205,224,236,365,407],"2":[207],"Overscript":[208,570],"Endscripts":[212,574],"zeta":[213,575],"m":[215,332,584],"Superscript":[216,222,232,400,405,578,581],"ind":[218,228,401],"Super":[219,229,402,580],"plus":[226,583],"right-parenthesis\">":[237,366,502],"<mml:mi>J</mml:mi>":[241],"<mml:mi>a</mml:mi>":[244,273,339],"<mml:mo>,</mml:mo>":[245,340],"<mml:mi>b</mml:mi>":[246,289,341],"<mml:munderover>":[251],"<mml:mo>\u2211</mml:mo>":[252],"<mml:mi>k</mml:mi>":[255,285,303,378,429,435],"</mml:munderover>":[265],"<mml:msubsup>":[266],"<mml:mspace":[271,274,290,418],"width=\"thinmathspace\"/>":[272,275,291,419],"<mml:mtext>ind</mml:mtext>":[277,293,370,421],"<mml:mo>+</mml:mo>":[288],"</mml:msubsup>":[307],"encoding=\"application/x-tex\">J_{a,b}=-\\sum":[310],"_{k=2}^{q-1}\\zeta":[311],"_m":[312],"^{\\,":[313],"a\\,":[314],"\\text":[315,317,439],"{ind}_{s}(k)+b\\,":[316],"{ind}_{s}(1-k)}</mml:annotation>":[318],"alttext=\"0":[326],"less-than-or-equal-to":[327,331],"<mml:mn>0</mml:mn>":[337],"<mml:mo>\u2264</mml:mo>":[338,342],"encoding=\"application/x-tex\">0\\leq":[348],"a,":[349],"b\\leq":[350],"m-1</mml:annotation>":[351],"where":[355],"alttext=\"ind":[360],"encoding=\"application/x-tex\">\\text":[383],"{ind}_{s}(k)</mml:annotation>":[384],"is":[388],"least":[390],"nonnegative":[391],"integer":[392],"such":[393],"that":[394,464],"k\">":[411],"<mml:msup>":[414],"</mml:msup>":[433],"encoding=\"application/x-tex\">s^{\\,":[438],"{ind}_{s}(k)}\\equiv":[440],"k</mml:annotation>":[441],"exhibit":[459],"set":[461],"properties":[463],"characterize":[465],"these":[466],"sums,":[467],"some":[468],"congruences":[469],"they":[470],"satisfy,":[471],"MAPLE":[474],"program":[475],"to":[476,484],"calculate":[477],"them.":[478],"Then":[479],"we":[480],"use":[481],"those":[482],"results":[483],"show":[485],"how":[486],"one":[487],"can":[488],"construct":[489],"families":[490],"P":[496],"x":[501],"<mml:mi>P</mml:mi>":[506],"<mml:mi>x</mml:mi>":[514],"encoding=\"application/x-tex\">P_{q}(x)</mml:annotation>":[519],"element-of":[528],"script":[529],"upper":[530],"P\">":[531],"<mml:mo>\u2208</mml:mo>":[535],"<mml:mi":[538],"class=\"MJX-tex-caligraphic\"":[539],"mathvariant=\"script\">P</mml:mi>":[540],"encoding=\"application/x-tex\">q\\in":[544],"\\mathcal":[545],"{P}</mml:annotation>":[546],"irreducible":[551],"polynomials":[552],"Gaussian":[554],"periods,":[555],"alttext=\"eta":[560],"i":[562,582],"j":[567],"0":[569],"j\">":[585],"<mml:semantic":[586]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}