Lukina, Olga Galois groups and Cantor actions. (English) Zbl 07313191 Trans. Am. Math. Soc. 374, No. 3, 1579-1621 (2021). MSC: 37B02 37B05 37P05 37C85 20E08 12F10 22A22 20E18 11R09 11R32 PDF BibTeX XML Cite \textit{O. Lukina}, Trans. Am. Math. Soc. 374, No. 3, 1579--1621 (2021; Zbl 07313191) Full Text: DOI
Reis, Lucas On the factorization of iterated polynomials. (English) Zbl 07318505 Rev. Mat. Iberoam. 36, No. 7, 1957-1978 (2020). MSC: 12E05 37P05 PDF BibTeX XML Cite \textit{L. Reis}, Rev. Mat. Iberoam. 36, No. 7, 1957--1978 (2020; Zbl 07318505) Full Text: DOI
Ferraguti, Andrea; Micheli, Giacomo An equivariant isomorphism theorem for \(\bmod\, \mathfrak{p}\) reductions of arboreal Galois representations. (English) Zbl 07301832 Trans. Am. Math. Soc. 373, No. 12, 8525-8542 (2020). MSC: 37P05 37P15 11G05 20E08 PDF BibTeX XML Cite \textit{A. Ferraguti} and \textit{G. Micheli}, Trans. Am. Math. Soc. 373, No. 12, 8525--8542 (2020; Zbl 07301832) Full Text: DOI
Goksel, Vefa On the orbit of a post-critically finite polynomial of the form \(x^d+c\). (English) Zbl 07225502 Funct. Approximatio, Comment. Math. 62, No. 1, 95-104 (2020). MSC: 11R09 37P15 PDF BibTeX XML Cite \textit{V. Goksel}, Funct. Approximatio, Comment. Math. 62, No. 1, 95--104 (2020; Zbl 07225502) Full Text: DOI Euclid
Looper, Nicole R. The \(ABC\)-conjecture implies uniform bounds on dynamical Zsigmondy sets. (English) Zbl 07215111 Trans. Am. Math. Soc. 373, No. 7, 4627-4647 (2020). Reviewer: Riccardo Pengo (Lyon) MSC: 11G50 11R32 37P15 14G05 37P45 PDF BibTeX XML Cite \textit{N. R. Looper}, Trans. Am. Math. Soc. 373, No. 7, 4627--4647 (2020; Zbl 07215111) Full Text: DOI
Demark, David; Hindes, Wade; Jones, Rafe; Misplon, Moses; Stoll, Michael; Stoneman, Michael Eventually stable quadratic polynomials over \(\mathbb{Q}\). (English) Zbl 1446.37100 New York J. Math. 26, 526-561 (2020). Reviewer: Artūras Dubickas (Vilnius) MSC: 37P15 11R09 37P05 12E05 11R32 11R45 PDF BibTeX XML Cite \textit{D. Demark} et al., New York J. Math. 26, 526--561 (2020; Zbl 1446.37100) Full Text: Link
Hindes, Wade; Jones, Rafe Riccati equations and polynomial dynamics over function fields. (English) Zbl 07174529 Trans. Am. Math. Soc. 373, No. 3, 1555-1575 (2020). Reviewer: Michael J. Jacobson jun. (Calgary) MSC: 11R32 37P15 14G05 PDF BibTeX XML Cite \textit{W. Hindes} and \textit{R. Jones}, Trans. Am. Math. Soc. 373, No. 3, 1555--1575 (2020; Zbl 07174529) Full Text: DOI
Li, Hua-Chieh Arboreal Galois representation for a certain type of quadratic polynomials. (English) Zbl 1435.37108 Arch. Math. 114, No. 3, 265-269 (2020). MSC: 37P05 11R32 11A07 PDF BibTeX XML Cite \textit{H.-C. Li}, Arch. Math. 114, No. 3, 265--269 (2020; Zbl 1435.37108) Full Text: DOI
Yamamoto, Kota On iterated extensions of number fields arising from quadratic polynomial maps. (English) Zbl 07152993 J. Number Theory 209, 289-311 (2020). MSC: 11R23 11R29 11R32 PDF BibTeX XML Cite \textit{K. Yamamoto}, J. Number Theory 209, 289--311 (2020; Zbl 07152993) Full Text: DOI
Gómez-Pérez, Domingo; Mérai, László; Shparlinski, Igor E. On the complexity of exact counting of dynamically irreducible polynomials. (English) Zbl 07151949 J. Symb. Comput. 99, 231-241 (2020). MSC: 11T06 11Y16 68W30 PDF BibTeX XML Cite \textit{D. Gómez-Pérez} et al., J. Symb. Comput. 99, 231--241 (2020; Zbl 07151949) Full Text: DOI arXiv
Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Silverman, Joseph H.; Tucker, Thomas J. Current trends and open problems in arithmetic dynamics. (English) Zbl 07124524 Bull. Am. Math. Soc., New Ser. 56, No. 4, 611-685 (2019). MSC: 37P05 37P15 37P20 37P25 37P30 37P45 37P55 PDF BibTeX XML Cite \textit{R. Benedetto} et al., Bull. Am. Math. Soc., New Ser. 56, No. 4, 611--685 (2019; Zbl 07124524) Full Text: DOI
Bridy, Andrew; Tucker, Thomas J. Finite index theorems for iterated Galois groups of cubic polynomials. (English) Zbl 07051737 Math. Ann. 373, No. 1-2, 37-72 (2019). MSC: 37P15 11G50 11R32 14G25 37P05 37P30 PDF BibTeX XML Cite \textit{A. Bridy} and \textit{T. J. Tucker}, Math. Ann. 373, No. 1--2, 37--72 (2019; Zbl 07051737) Full Text: DOI arXiv
D’Andrea, Carlos; Ostafe, Alina; Shparlinski, Igor E.; Sombra, Martín Reductions modulo primes of systems of polynomial equations and algebraic dynamical systems. (English) Zbl 1403.37101 Trans. Am. Math. Soc. 371, No. 2, 1169-1198 (2019). MSC: 37P05 11G25 11G35 13P15 37P25 PDF BibTeX XML Cite \textit{C. D'Andrea} et al., Trans. Am. Math. Soc. 371, No. 2, 1169--1198 (2019; Zbl 1403.37101) Full Text: DOI arXiv
Juul, J. Iterates of generic polynomials and generic rational functions. (English) Zbl 1442.37120 Trans. Am. Math. Soc. 371, No. 2, 809-831 (2019). MSC: 37P05 11G35 14G25 11R45 12F10 12E05 PDF BibTeX XML Cite \textit{J. Juul}, Trans. Am. Math. Soc. 371, No. 2, 809--831 (2019; Zbl 1442.37120) Full Text: DOI
Hindes, Wade Average Zsigmondy sets, dynamical Galois groups, and the Kodaira-Spencer map. (English) Zbl 1394.37130 Trans. Am. Math. Soc. 370, No. 9, 6391-6410 (2018). Reviewer: Franco Vivaldi (London) MSC: 37P15 11R32 11B37 14G05 PDF BibTeX XML Cite \textit{W. Hindes}, Trans. Am. Math. Soc. 370, No. 9, 6391--6410 (2018; Zbl 1394.37130) Full Text: DOI arXiv
Hindes, Wade Classifying Galois groups of small iterates via rational points. (English) Zbl 1441.11281 Int. J. Number Theory 14, No. 5, 1403-1426 (2018). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R32 11G30 14G05 37P15 PDF BibTeX XML Cite \textit{W. Hindes}, Int. J. Number Theory 14, No. 5, 1403--1426 (2018; Zbl 1441.11281) Full Text: DOI arXiv
Ferraguti, Andrea The set of stable primes for polynomial sequences with large Galois group. (English) Zbl 1442.11150 Proc. Am. Math. Soc. 146, No. 7, 2773-2784 (2018). MSC: 11R32 11R45 20E08 PDF BibTeX XML Cite \textit{A. Ferraguti}, Proc. Am. Math. Soc. 146, No. 7, 2773--2784 (2018; Zbl 1442.11150) Full Text: DOI arXiv
Benedetto, Robert L.; Faber, Xander; Hutz, Benjamin; Juul, Jamie; Yasufuku, Yu A large arboreal Galois representation for a cubic postcritically finite polynomial. (English) Zbl 1427.11118 Res. Number Theory 3, Paper No. 29, 21 p. (2017). MSC: 11R32 05C25 11R09 PDF BibTeX XML Cite \textit{R. L. Benedetto} et al., Res. Number Theory 3, Paper No. 29, 21 p. (2017; Zbl 1427.11118) Full Text: DOI
Jones, Rafe; Levy, Alon Eventually stable rational functions. (English) Zbl 1391.37072 Int. J. Number Theory 13, No. 9, 2299-2318 (2017). MSC: 37P05 37P15 11R32 12E05 37P25 11S82 PDF BibTeX XML Cite \textit{R. Jones} and \textit{A. Levy}, Int. J. Number Theory 13, No. 9, 2299--2318 (2017; Zbl 1391.37072) Full Text: DOI arXiv
Hindes, Wade Prime divisors in polynomial orbits over function fields. (English) Zbl 1367.14009 Bull. Lond. Math. Soc. 48, No. 6, 1029-1036 (2016). Reviewer: Yu Yasufuku (Tokyo) (MR3608948) MSC: 14H05 11R32 14G05 14H25 37P55 PDF BibTeX XML Cite \textit{W. Hindes}, Bull. Lond. Math. Soc. 48, No. 6, 1029--1036 (2016; Zbl 1367.14009) Full Text: DOI arXiv
Ostafe, Alina On some extensions of the Ailon-Rudnick theorem. (English) Zbl 1355.11103 Monatsh. Math. 181, No. 2, 451-471 (2016). Reviewer: Gabriel D. Villa-Salvador (México D. F.) MSC: 11R58 11D61 PDF BibTeX XML Cite \textit{A. Ostafe}, Monatsh. Math. 181, No. 2, 451--471 (2016; Zbl 1355.11103) Full Text: DOI arXiv
Hindes, Wade The Vojta conjecture implies Galois rigidity in dynamical families. (English) Zbl 1338.14026 Proc. Am. Math. Soc. 144, No. 5, 1931-1938 (2016). Reviewer: Yu Yasufuku (Tokyo) MSC: 14G05 37P45 11R32 37P05 11J97 37P55 PDF BibTeX XML Cite \textit{W. Hindes}, Proc. Am. Math. Soc. 144, No. 5, 1931--1938 (2016; Zbl 1338.14026) Full Text: DOI arXiv
Swaminathan, Ashvin A. On arboreal Galois representations of rational functions. (English) Zbl 1387.11081 J. Algebra 448, 104-126 (2016). Reviewer: Nuria Vila (Barcelona) MSC: 11R32 12F10 37P15 11F80 PDF BibTeX XML Cite \textit{A. A. Swaminathan}, J. Algebra 448, 104--126 (2016; Zbl 1387.11081) Full Text: DOI
Hindes, Wade The arithmetic of curves defined by iteration. (English) Zbl 1330.14032 Acta Arith. 169, No. 1, 1-27 (2015). Reviewer: Yu Yasufuku (Tokyo) MSC: 14G05 37P05 12F10 37P15 11G30 11G05 14H45 20E08 37P55 14H25 PDF BibTeX XML Cite \textit{W. Hindes}, Acta Arith. 169, No. 1, 1--27 (2015; Zbl 1330.14032) Full Text: DOI arXiv
Jones, Rafe Fixed-point-free elements of iterated monodromy groups. (English) Zbl 1385.37063 Trans. Am. Math. Soc. 367, No. 3, 2023-2049 (2015). MSC: 37F10 20E08 37P05 37F20 PDF BibTeX XML Cite \textit{R. Jones}, Trans. Am. Math. Soc. 367, No. 3, 2023--2049 (2015; Zbl 1385.37063) Full Text: DOI arXiv
Hindes, Wade Galois uniformity in quadratic dynamics over \(k(t)\). (English) Zbl 1391.37090 J. Number Theory 148, 372-383 (2015). MSC: 37P55 14G05 PDF BibTeX XML Cite \textit{W. Hindes}, J. Number Theory 148, 372--383 (2015; Zbl 1391.37090) Full Text: DOI arXiv
Benedetto, Robert L.; Ghioca, Dragos; Hutz, Benjamin; Kurlberg, Pär; Scanlon, Thomas; Tucker, Thomas J. Periods of rational maps modulo primes. (English) Zbl 1317.37111 Math. Ann. 355, No. 2, 637-660 (2013). Reviewer: Paul Vojta (Berkeley) MSC: 37P05 37P15 PDF BibTeX XML Cite \textit{R. L. Benedetto} et al., Math. Ann. 355, No. 2, 637--660 (2013; Zbl 1317.37111) Full Text: DOI arXiv
Jones, Rafe An iterative construction of irreducible polynomials reducible modulo every prime. (English) Zbl 1302.11086 J. Algebra 369, 114-128 (2012). MSC: 11R09 37P15 PDF BibTeX XML Cite \textit{R. Jones}, J. Algebra 369, 114--128 (2012; Zbl 1302.11086) Full Text: DOI arXiv
Jones, Rafe; Boston, Nigel Settled polynomials over finite fields. (English) Zbl 1243.11115 Proc. Am. Math. Soc. 140, No. 6, 1849-1863 (2012); erratum ibid. 148, No. 2, 913-914 (2020). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11T06 11C08 37P25 60J99 PDF BibTeX XML Cite \textit{R. Jones} and \textit{N. Boston}, Proc. Am. Math. Soc. 140, No. 6, 1849--1863 (2012; Zbl 1243.11115) Full Text: DOI
Ahmadi, Omran; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E. On stable quadratic polynomials. (English) Zbl 1241.11027 Glasg. Math. J. 54, No. 2, 359-369 (2012). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11C08 11T06 37P05 PDF BibTeX XML Cite \textit{O. Ahmadi} et al., Glasg. Math. J. 54, No. 2, 359--369 (2012; Zbl 1241.11027) Full Text: DOI
Benedetto, Robert L.; Ghioca, Dragos; Kurlberg, Pär; Tucker, Thomas J. A case of the dynamical Mordell-Lang conjecture. (English) Zbl 1285.37021 Math. Ann. 352, No. 1, 1-26 (2012). Reviewer: Paul Vojta (Berkeley) MSC: 37P55 37P20 PDF BibTeX XML Cite \textit{R. L. Benedetto} et al., Math. Ann. 352, No. 1, 1--26 (2012; Zbl 1285.37021) Full Text: DOI
Faber, Xander; Granville, Andrew Prime factors of dynamical sequences. (English) Zbl 1290.11019 J. Reine Angew. Math. 661, 189-214 (2011). Reviewer: Pieter Moree (Bonn) MSC: 11B37 37P05 PDF BibTeX XML Cite \textit{X. Faber} and \textit{A. Granville}, J. Reine Angew. Math. 661, 189--214 (2011; Zbl 1290.11019) Full Text: DOI arXiv
Sookdeo, Vijay A. Integer points in backward orbits. (English) Zbl 1246.37102 J. Number Theory 131, No. 7, 1229-1239 (2011). MSC: 37P35 11S82 PDF BibTeX XML Cite \textit{V. A. Sookdeo}, J. Number Theory 131, No. 7, 1229--1239 (2011; Zbl 1246.37102) Full Text: DOI arXiv
Gottesman, Richard; Tang, Kwokfung Quadratic recurrences with a positive density of prime divisors. (English) Zbl 1244.11014 Int. J. Number Theory 6, No. 5, 1027-1045 (2010). MSC: 11B37 12F10 37P05 PDF BibTeX XML Cite \textit{R. Gottesman} and \textit{K. Tang}, Int. J. Number Theory 6, No. 5, 1027--1045 (2010; Zbl 1244.11014) Full Text: DOI
Ostafe, Alina; Shparlinski, Igor E. On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators. (English) Zbl 1227.11093 Math. Comput. 79, No. 269, 501-511 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11K45 11T23 37A45 37F10 PDF BibTeX XML Cite \textit{A. Ostafe} and \textit{I. E. Shparlinski}, Math. Comput. 79, No. 269, 501--511 (2010; Zbl 1227.11093) Full Text: DOI arXiv
Ostafe, Alina; Shparlinski, Igor E. On the length of critical orbits of stable quadratic polynomials. (English) Zbl 1268.11155 Proc. Am. Math. Soc. 138, No. 8, 2653-2656 (2010). MSC: 11T06 37P25 11L40 PDF BibTeX XML Cite \textit{A. Ostafe} and \textit{I. E. Shparlinski}, Proc. Am. Math. Soc. 138, No. 8, 2653--2656 (2010; Zbl 1268.11155) Full Text: DOI arXiv
Ostafe, Alina; Shparlinski, Igor E. Pseudorandom numbers and hash functions from iterations of multivariate polynomials. (English) Zbl 1185.11049 Cryptogr. Commun. 2, No. 1, 49-67 (2010). Reviewer: Arne Winterhof (Linz) MSC: 11K45 11T23 65C10 94A60 PDF BibTeX XML Cite \textit{A. Ostafe} and \textit{I. E. Shparlinski}, Cryptogr. Commun. 2, No. 1, 49--67 (2010; Zbl 1185.11049) Full Text: DOI arXiv
Boston, Nigel; Jones, Rafe Arboreal Galois representations. (English) Zbl 1206.11069 Geom. Dedicata 124, 27-35 (2007). MSC: 11F80 11R32 20E08 20E18 PDF BibTeX XML Cite \textit{N. Boston} and \textit{R. Jones}, Geom. Dedicata 124, 27--35 (2007; Zbl 1206.11069) Full Text: DOI