Han, Minsik Misiurewicz polynomials for rational maps with nontrivial automorphisms. (English) Zbl 1469.37067 Acta Arith. 198, No. 3, 257-274 (2021). For a given integer \(d \geq 2\) the author defines a Misiurewicz polynomial \(G_m\) for \(m=1,2,\dots\). For example, for \(d=3\) we have \(G_1=-a-6\) and \[ G_2=-a^6-a^5-30a^4-144a^3-216a^2-648a-1944. \] He shows that for each prime number \(d \geq 3\) the \(m\)-th Misiurewicz polynomial \(G_m\) is irreducible over \(\mathbb Q\) for \(m=1,2,3\). The proof is based on the theory of Newton polygons. Reviewer: Artūras Dubickas (Vilnius) MSC: 37P05 Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps 37P45 Families and moduli spaces in arithmetic and non-Archimedean dynamical systems 11R09 Polynomials (irreducibility, etc.) Keywords:arithmetic dynamics; rational maps; automorphisms; Gleason polynomials; Misiurewicz polynomials; irreducibility PDFBibTeX XMLCite \textit{M. Han}, Acta Arith. 198, No. 3, 257--274 (2021; Zbl 1469.37067) Full Text: DOI arXiv References: [1] R. Benedetto, P. Ingram, R. Jones, M. Manes, J. H. Silverman, and T. J. Tucker, Current trends and open problems in arithmetic dynamics, Bull. Amer. Math. Soc. 56 (2019), 611-685. · Zbl 1468.37001 [2] X. Buff,On postcritically finite unicritical polynomials, New York J. Math. 24 (2018), 1111-1122. · Zbl 1412.37084 [3] X. Buff, A. L. Epstein, and S. Koch,Rational maps with a preperiodic critical point, arXiv:1806.11221 (2018). [4] A. Epstein,Integrality and rigidity for postcritically finite polynomials(with an appendix by A. Epstein and B. Poonen), Bull. London Math. Soc. 44 (2012), 39-46. · Zbl 1291.37057 [5] V. Goksel,On the orbit of a post-critically finite polynomial of the formxd+c, Funct. Approx. Comment. Math. 62 (2020), 95-104. · Zbl 1506.11141 [6] V. Goksel,A note on Misiurewicz polynomials, J. Théor. Nombres Bordeaux 32 (2020), 373-385. · Zbl 1460.11124 [7] B. Hutz and A. Towsley,Misiurewicz points for polynomial maps and transversality, New York J. Math. 21 (2015), 297-319. · Zbl 1391.37071 [8] N. Koblitz,p-adic Numbers,p-adic Analysis, and Zeta-Functions, 2nd ed., Grad. Texts in Math. 58, Springer, New York, 2012. · Zbl 0364.12015 [9] N. Miasnikov, B. Stout, and P. Williams,Automorphism loci for the moduli space of rational maps, Acta Arith. 180 (2017), 267-296. · Zbl 1391.37085 [10] J. H. Silverman,The Arithmetic of Dynamical Systems, Grad. Texts in Math. 241, Springer, New York, 2007. · Zbl 1130.37001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.