{"title":"Dynamical Irreducibility of Certain Families of Polynomials over Finite Fields","authors":"Tori Day, Rebecca DeLand, Jamie Juul, Cigole Thomas, Bianca Thompson, Bella Tobin","doi":"arxiv-2409.10467","DOIUrl":null,"url":null,"abstract":"We determine necessary and sufficient conditions for unicritical polynomials\nto be dynamically irreducible over finite fields. This result extends the\nresults of Boston-Jones and Hamblen-Jones-Madhu regarding the dynamical\nirreducibility of particular families of unicritical polynomials. We also\ninvestigate dynamical irreducibility conditions for cubic and shifted\nlinearized polynomials.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Number Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10467","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We determine necessary and sufficient conditions for unicritical polynomials
to be dynamically irreducible over finite fields. This result extends the
results of Boston-Jones and Hamblen-Jones-Madhu regarding the dynamical
irreducibility of particular families of unicritical polynomials. We also
investigate dynamical irreducibility conditions for cubic and shifted
linearized polynomials.
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