## 7 Citations

### Finite index theorems for iterated Galois groups of unicritical polynomials

- Mathematics
- 2018

Let $K$ be the function field of a smooth, irreducible curve defined over $\overline{\mathbb{Q}}$. Let $f\in K[x]$ be of the form $f(x)=x^q+c$ where $q = p^{r}, r \ge 1,$ is a power of the prime…

### Finite index theorems for iterated Galois groups of cubic polynomials

- Mathematics
- 2017

Let K be a number field or a function field. Let $$f\in K(x)$$f∈K(x) be a rational function of degree $$d\ge 2$$d≥2, and let $$\beta \in {\mathbb {P}}^1(\overline{K})$$β∈P1(K¯). For all $$n\in…

### The Arakelov-Zhang pairing and Julia sets

- MathematicsProceedings of the American Mathematical Society
- 2021

The Arakelov-Zhang pairing $\langle\psi,\phi\rangle$ is a measure of the "dynamical distance" between two rational maps $\psi$ and $\phi$ defined over a number field $K$. It is defined in terms of…

### Integral points in orbits in characteristic $p$

- Mathematics
- 2021

We prove a characteristic p version of a theorem of Silverman on integral points in orbits over number fields and establish a primitive prime divisor theorem for polynomials in this setting. In…

### Zsigmondy theorem for arithmetic dynamics induced by a drinfeld module

- Mathematics, ArtInternational Journal of Number Theory
- 2019

Let [Formula: see text] be a Drinfeld [Formula: see text]-module defined over a global function field [Formula: see text] Let [Formula: see text] be a non-torsion point of [Formula: see text] with…

### Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups

- MathematicsInternational Mathematics Research Notices
- 2019

We study multiplicative dependence between elements in orbits of algebraic dynamical systems over number fields modulo a finitely generated multiplicative subgroup of the field. We obtain a series…

### Finite index theorems for iterated Galois groups of cubic polynomials

- Materials ScienceMathematische Annalen
- 2018

Let K be a number field or a function field. Let f∈K(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…

## References

SHOWING 1-10 OF 25 REFERENCES

### FINITE RAMIFICATION FOR PREIMAGE FIELDS OF POSTCRITICALLY FINITE MORPHISMS

- Mathematics
- 2015

Given a finite endomorphism $\varphi$ of a variety $X$ defined over the field of fractions $K$ of a Dedekind domain, we study the extension $K(\varphi^{-\infty}(\alpha)) : = \bigcup_{n \geq 1}…

### Periods of rational maps modulo primes

- Mathematics
- 2011

Let K be a number field, let $${\varphi \in K(t)}$$ be a rational map of degree at least 2, and let $${\alpha, \beta \in K}$$ . We show that if α is not in the forward orbit of β, then there is a…

### ABC implies primitive prime divisors in arithmetic dynamics

- Mathematics
- 2013

Let K be a number field, let φ(x)∈K(x) be a rational function of degree d>1, and let α∈K be a wandering point such that φn(α)≠0 for all n>0. We prove that if the abc‐conjecture holds for K, then for…

### A finiteness theorem for canonical heights attached to rational maps over function fields

- Mathematics
- 2006

Abstract Let K be a function field, let φ ∈ K(T) be a rational map of degree d ≧ 2 defined over K, and suppose that φ is not isotrivial. In this paper, we show that a point P ∈ ℙ1 () has φ-canonical…

### Iterates of Generic Polynomials and Generic Rational Functions

- Mathematics
- 2014

In 1985, Odoni showed that in characteristic $0$ the Galois group of the $n$-th iterate of the generic polynomial with degree $d$ is as large as possible. That is, he showed that this Galois group is…

### Galois groups over $$cQ$$ of some iterated polynomials

- Mathematics
- 1992

0. Introduction. Throughout this paper, a will denote an integer such that a is not a square in Q, f : = X 2 + a e 2g [X], and f0 : = X, f , + 1 : = f (f,) = f 2 + a for all n > 0, are 2 the iterates…

### Heights and preperiodic points of polynomials over function fields

- Mathematics
- 2005

Let K be a function field in one variable over an arbitrary field F. Given a rational function f(z) in K(z) of degree at least two, the associated canonical height on the projective line was defined…

### Primitive prime divisors in the critical orbit of z^d+c

- Mathematics
- 2012

We prove the finiteness of the Zsigmondy set associated to the critical orbit of f(z) = z^d+c for rational values of c by finding an effective bound on the size of the set. For non-recurrent critical…

### Realising wreath products of cyclic groups as Galois groups

- Mathematics
- 1988

Let K be any field of characteristic 0 and let T and X be algebraically independent over K . For n ≥ 1 let k ( n ) ≥ 2 be an integer and let fn ( X , T ) = x k(n) + T e K [ X , T ]. We shall regard T…

### Prime factors of dynamical sequences

- Mathematics
- 2009

Abstract Let (t) (t) have degree d 2. For a given rational number x0, define xn1 (xn) for each n 0. If this sequence is not eventually periodic, and if does not lie in one of two explicitly…