## The density of prime divisors in the arithmetic dynamics of quadratic polynomials

- Rafe Jones
- Mathematics
- 14 December 2006

Let f ∈ ℤ[x], and consider the recurrence given by an = f(an − 1), with a0 ∈ ℤ. Denote by P(f, a0) the set of prime divisors of this recurrence, that is, the set of primes dividing at least one… Expand

## Galois representations from pre-image trees: an arboreal survey

- Rafe Jones
- Mathematics
- 24 February 2014

Given a global field K and a rational function phi defined over K, one may take pre-images of 0 under successive iterates of phi, and thus obtain an infinite rooted tree T by assigning edges… Expand

## Settled polynomials over finite fields

- Rafe Jones, N. Boston
- Mathematics
- 1 June 2012

We study the factorization into irreducibles of iterates of a qua- dratic polynomial f over a nite eld. We call f settled when the factorization of its nth iterate for large n is dominated by… Expand

## Achievement Sets of Sequences

- Rafe Jones
- MathematicsThe American mathematical monthly
- 1 June 2011

## Eventually stable rational functions

- Rafe Jones, Alon Y. Levy
- Mathematics
- 2 March 2016

For a field K, rational function phi in K(z) of degree at least two, and alpha in P^1(K), we study the polynomials in K[z] whose roots are given by the solutions to phi^n(z) = alpha, where phi^n… Expand

## Galois theory of iterated endomorphisms

- Rafe Jones, Jeremy A. Rouse
- Mathematics
- 15 June 2007

Given an abelian algebraic group A over a global field F, α ∈ A(F), and a prime ℓ, the set of all preimages of α under some iterate of [ℓ] generates an extension of F that contains all ℓ‐power… Expand

## Galois theory of quadratic rational functions

- Rafe Jones, M. Manes
- Mathematics
- 23 January 2011

For a number field K with absolute Galois group G_K, we consider the action of G_K on the infinite tree of preimages of a point in K under a degree-two rational function phi, with particular… Expand

## An iterative construction of irreducible polynomials reducible modulo every prime

- Rafe Jones
- Mathematics
- 13 December 2010

## Arboreal Galois representations

- N. Boston, Rafe Jones
- Mathematics
- 16 January 2007

Let $$G_{\mathbb{Q}}$$ be the absolute Galois group of $$\mathbb{Q}$$, and let T be the complete rooted d-ary tree, where d ≥ 2. In this article, we study “arboreal” representations of… Expand

## The Density of Primes in Orbits of zd+c

- Spencer Hamblen, Rafe Jones, Kalyani Madhu
- Mathematics
- 26 March 2013

Given a polynomial f(z) = z^d + c over a global field K and a_0 in K, we study the density of prime ideals of K dividing at least one element of the orbit of a_0 under f. The density of such sets for… Expand

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