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D. Wan very recently proved an asymptotic version of a conjecture of Hansen and Mullen concerning the distribution of irreducible polynomials over finite fields. In this note we prove that the conjecture is true in general by using machine calculation to verify the open cases remaining after Wan\u2019s work.<\/p>","DOI":"10.1090\/s0025-5718-98-00904-1","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T22:14:44Z","timestamp":1027721684000},"page":"337-341","source":"Crossref","is-referenced-by-count":19,"title":["Distribution of irreducible polynomials of small degrees over finite fields"],"prefix":"10.1090","volume":"67","author":[{"given":"Kie","family":"Ham","sequence":"first","affiliation":[]},{"given":"Gary","family":"Mullen","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0012-365X(90)90215-4","article-title":"Primitive elements and polynomials with arbitrary trace","volume":"83","author":"Cohen, Stephen D.","year":"1990","journal-title":"Discrete Math.","ISSN":"http:\/\/id.crossref.org\/issn\/0012-365X","issn-type":"print"},{"key":"2","first-page":"43","article-title":"Primitive elements and polynomials: existence results","author":"Cohen, Stephen D.","year":"1993"},{"issue":"213","key":"3","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1090\/S0025-5718-96-00663-1","article-title":"The coefficients of primitive polynomials over finite fields","volume":"65","author":"Han, Wen Bao","year":"1996","journal-title":"Math. Comp.","ISSN":"http:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"200","key":"4","doi-asserted-by":"publisher","first-page":"639","DOI":"10.2307\/2153081","article-title":"Primitive polynomials over finite fields","volume":"59","author":"Hansen, Tom","year":"1992","journal-title":"Math. Comp.","ISSN":"http:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"5","series-title":"Encyclopedia of Mathematics and its Applications","isbn-type":"print","volume-title":"Finite fields","volume":"20","author":"Lidl, Rudolf","year":"1983","ISBN":"http:\/\/id.crossref.org\/isbn\/0201135191"},{"key":"6","doi-asserted-by":"crossref","unstructured":"D. Wan, Generators and irreducible polynomials over finite fields, Math. Comp. 66 (1997), 1195\u20131212.","DOI":"10.1090\/S0025-5718-97-00835-1"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1998-67-221\/S0025-5718-98-00904-1\/S0025-5718-98-00904-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-221\/S0025-5718-98-00904-1\/S0025-5718-98-00904-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,2]],"date-time":"2021-11-02T23:37:54Z","timestamp":1635896274000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-221\/S0025-5718-98-00904-1\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998]]},"references-count":6,"journal-issue":{"issue":"221","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["S0025-5718-98-00904-1"],"URL":"http:\/\/dx.doi.org\/10.1090\/s0025-5718-98-00904-1","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["0025-5718","1088-6842"],"issn-type":[{"value":"0025-5718","type":"print"},{"value":"1088-6842","type":"electronic"}],"subject":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"published":{"date-parts":[[1998]]}}}