Settled polynomials over finite fields

DOI10.1090/S0002-9939-2011-11054-2zbMath1243.11115MaRDI QIDQ2884407

Nigel Boston, Rafe Jones

Publication date: 29 May 2012

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

irreducible polynomialspolynomial iteratessettled polynomials

Mathematics Subject Classification ID

Polynomials in number theory (11C08) Polynomials over finite fields (11T06) Markov processes (60J99) Dynamical systems over finite ground fields (37P25)

Related Items (22)

On the existence of infinite, non-trivial \(F\)-sets ⋮ On some extensions of the Ailon-Rudnick theorem ⋮ An estimate on the number of stable quadratic polynomials ⋮ Settled elements in profinite groups ⋮ Eventually stable rational functions ⋮ A new direction on constructing irreducible polynomials over finite fields ⋮ An iterative construction of irreducible polynomials reducible modulo every prime ⋮ Arboreal Representations for Rational Maps with Few Critical Points ⋮ On the factorization of iterated polynomials ⋮ On the length of critical orbits of stable quadratic polynomials ⋮ Counting periodic points on quotient varieties over \(\mathbb{F}_q\) ⋮ On the complexity of exact counting of dynamically irreducible polynomials ⋮ Irreducibility of iterates of post-critically finite quadratic polynomials over \(\mathbb{Q}\) ⋮ Dynamical irreducibility of polynomials modulo primes ⋮ Errata to “Settled polynomials over finite fields” ⋮ A Refined Conjecture for Factorizations of Iterates of Quadratic Polynomials over Finite Fields ⋮ A note on the stability of trinomials over finite fields ⋮ Irreducible polynomials over finite fields produced by composition of quadratics ⋮ Markov processes and some PCF quadratic polynomials ⋮ Current trends and open problems in arithmetic dynamics ⋮ Newly reducible polynomial iterates ⋮ On Sets of Irreducible Polynomials Closed by Composition

Cites Work

• Non-negative matrices and Markov chains. 2nd ed
• Arboreal Galois representations
• On the irreducibility of the iterates of 𝑥ⁿ-𝑏
• The density of prime divisors in the arithmetic dynamics of quadratic polynomials
• On the length of critical orbits of stable quadratic polynomials
• The Transitive Permutation Groups of Degree 32
• Irreducibility of the iterates of a quadratic polynomial over a field
• Properties of Iterates and Composites of Polynomials
• Stabilité des polynômes
• Iterated Galois towers, their associated martingales, and the $p$-adic Mandelbrot set

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