{"id":"https://openalex.org/W2083038126","doi":"https://doi.org/10.1090/s0025-5718-01-01375-8","title":"The irreducibility of some level 1 Hecke polynomials","display_name":"The irreducibility of some level 1 Hecke polynomials","publication_year":2001,"publication_date":"2001-06-22","ids":{"openalex":"https://openalex.org/W2083038126","doi":"https://doi.org/10.1090/s0025-5718-01-01375-8","mag":"2083038126"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01375-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01375-8","pdf_url":"https://www.ams.org/mcom/2002-71-239/S0025-5718-01-01375-8/S0025-5718-01-01375-8.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/2002-71-239/S0025-5718-01-01375-8/S0025-5718-01-01375-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112256447","display_name":"David W. Farmer","orcid":null},"institutions":[{"id":"https://openalex.org/I131221577","display_name":"Bucknell University","ror":"https://ror.org/00fc1qt65","country_code":"US","type":"education","lineage":["https://openalex.org/I131221577"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D. Farmer","raw_affiliation_strings":["Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837","institution_ids":["https://openalex.org/I131221577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030115432","display_name":"Kevin James","orcid":"https://orcid.org/0000-0002-2049-7697"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"K. James","raw_affiliation_strings":["Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975","Department of Mathematical Sciences; Clemson University; Clemson; South Carolina; 29634-0975"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975","institution_ids":["https://openalex.org/I8078737"]},{"raw_affiliation_string":"Department of Mathematical Sciences; Clemson University; Clemson; South Carolina; 29634-0975","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112256447"],"corresponding_institution_ids":["https://openalex.org/I131221577"],"apc_list":null,"apc_paid":null,"fwci":1.4698,"has_fulltext":true,"cited_by_count":29,"citation_normalized_percentile":{"value":0.80156731,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"71","issue":"239","first_page":"1263","last_page":"1270"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9994999766349792,"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":0.9991999864578247,"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":0.9383682608604431},{"id":"https://openalex.org/keywords/irreducibility","display_name":"Irreducibility","score":0.8704713582992554},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6186456680297852},{"id":"https://openalex.org/keywords/galois-group","display_name":"Galois group","score":0.5719026923179626},{"id":"https://openalex.org/keywords/cusp","display_name":"Cusp (singularity)","score":0.552172064781189},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.504243016242981},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4416036307811737},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4286741018295288},{"id":"https://openalex.org/keywords/hecke-operator","display_name":"Hecke operator","score":0.4197629392147064},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1492103636264801},{"id":"https://openalex.org/keywords/modular-form","display_name":"Modular form","score":0.1432247757911682},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09625005722045898}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9383682608604431},{"id":"https://openalex.org/C2776823524","wikidata":"https://www.wikidata.org/wiki/Q6073561","display_name":"Irreducibility","level":2,"score":0.8704713582992554},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6186456680297852},{"id":"https://openalex.org/C67536143","wikidata":"https://www.wikidata.org/wiki/Q730384","display_name":"Galois group","level":2,"score":0.5719026923179626},{"id":"https://openalex.org/C2778400075","wikidata":"https://www.wikidata.org/wiki/Q655275","display_name":"Cusp (singularity)","level":2,"score":0.552172064781189},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.504243016242981},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4416036307811737},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4286741018295288},{"id":"https://openalex.org/C41217588","wikidata":"https://www.wikidata.org/wiki/Q1592959","display_name":"Hecke operator","level":3,"score":0.4197629392147064},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1492103636264801},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.1432247757911682},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09625005722045898}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-01-01375-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01375-8","pdf_url":"https://www.ams.org/mcom/2002-71-239/S0025-5718-01-01375-8/S0025-5718-01-01375-8.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:10.1.1.154.3661","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.3661","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/mcom/2002-71-239/S0025-5718-01-01375-8/S0025-5718-01-01375-8.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.329.4231","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.4231","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sage.math.washington.edu/msri06/refs/FarmerJames2000.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.36.7374","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.7374","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://farmer.bucknell.edu/~farmer/Papers/FarmerJames2000.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01375-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01375-8","pdf_url":"https://www.ams.org/mcom/2002-71-239/S0025-5718-01-01375-8/S0025-5718-01-01375-8.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":[{"id":"https://openalex.org/F4320307521","display_name":"American Institute of Mathematics","ror":"https://ror.org/02a0fwv66"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2083038126.pdf","grobid_xml":"https://content.openalex.org/works/W2083038126.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1496801598","https://openalex.org/W1575834508","https://openalex.org/W1589201628","https://openalex.org/W1980939000","https://openalex.org/W1996183350","https://openalex.org/W2011496643","https://openalex.org/W2052624439","https://openalex.org/W2071483197","https://openalex.org/W2107384180","https://openalex.org/W2140283762","https://openalex.org/W2162442687","https://openalex.org/W2325231713","https://openalex.org/W4235419309","https://openalex.org/W4297756508","https://openalex.org/W6638347121","https://openalex.org/W6732987287","https://openalex.org/W6828012568"],"related_works":["https://openalex.org/W2031316819","https://openalex.org/W2738869349","https://openalex.org/W2767033796","https://openalex.org/W2013548473","https://openalex.org/W4290067084","https://openalex.org/W2032299356","https://openalex.org/W4283157311","https://openalex.org/W2225342623","https://openalex.org/W2065795422","https://openalex.org/W2033649860"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,45,75,111,155,175,197,216],"content-type=\"math/mathml\">":[2,46,76,112,156,176,198,217],"<mml:math":[3,47,77,113,157,177,199,218],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,48,78,114,158,178,200,219],"alttext=\"upper":[5,49,79,115],"T":[6,50,116],"Subscript":[7,51,81,117],"p":[8,118],"comma":[9,119],"k":[10,82,120],"Baseline":[11,83,121],"left-parenthesis":[12,84,122],"x":[13,123],"right-parenthesis\">":[14,86,124],"<mml:semantics>":[15,53,87,125,162,182,204,221],"<mml:mrow>":[16,88,126,183,205],"<mml:msub>":[17,54,89,127],"<mml:mi>T</mml:mi>":[18,55,128],"<mml:mrow":[19,56,91,129,163],"class=\"MJX-TeXAtom-ORD\">":[20,57,92,130,164],"<mml:mi>p</mml:mi>":[21,58,131,206,222],"<mml:mo>,</mml:mo>":[22,132],"<mml:mi>k</mml:mi>":[23,93,133,184],"</mml:mrow>":[24,31,59,94,101,134,141,167,189,209],"</mml:msub>":[25,60,95,135],"<mml:mo":[26,29,96,99,136,139],"stretchy=\"false\">(</mml:mo>":[27,97,137],"<mml:mi>x</mml:mi>":[28,138],"stretchy=\"false\">)</mml:mo>":[30,100,140],"<mml:annotation":[32,61,102,142,168,190,210,223],"encoding=\"application/x-tex\">T_{p,k}(x)</mml:annotation>":[33,143],"</mml:semantics>":[34,63,104,144,171,193,212,225],"</mml:math>":[35,64,105,145,172,194,213,226],"</inline-formula>":[36,65,106,146,173,195,214,227],"be":[37],"the":[38,42,68],"characteristic":[39],"polynomial":[40],"of":[41,70],"Hecke":[43],"operator":[44],"p\">":[52],"encoding=\"application/x-tex\">T_{p}</mml:annotation>":[62],"acting":[66],"on":[67],"space":[69],"level":[71],"1":[72,85],"cusp":[73],"forms":[74],"S":[80],"<mml:mi>S</mml:mi>":[90],"<mml:mn>1</mml:mn>":[98],"encoding=\"application/x-tex\">S_{k}(1)</mml:annotation>":[103],".":[107],"We":[108],"show":[109],"that":[110],"is":[147],"irreducible":[148],"and":[149,196],"has":[150],"full":[151],"Galois":[152],"group":[153],"over":[154],"alttext=\"bold":[159],"upper":[160],"Q\">":[161],"<mml:mi":[165],"mathvariant=\"bold\">Q</mml:mi>":[166],"encoding=\"application/x-tex\">\\mathbf":[169],"{Q}</mml:annotation>":[170],"for":[174],"alttext=\"k":[179],"less-than-or-equal-to":[180],"2000\">":[181,203],"<mml:mo>":[185],"\u2264":[186],"</mml:mo>":[187],"<mml:mn>2000</mml:mn>":[188,208],"encoding=\"application/x-tex\">k\\le":[191],"2000</mml:annotation>":[192],"alttext=\"p":[201],"greater-than":[202],"<mml:mo>&gt;</mml:mo>":[207],"encoding=\"application/x-tex\">p&gt;2000</mml:annotation>":[211],",":[215],"alttext=\"p\">":[220],"encoding=\"application/x-tex\">p</mml:annotation>":[224],"prime.":[228]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
