Andrew Bridy

activity

20122021

most citedAutomatic Sequences and Curves over Finite Fields

13 citations · 31 across the 9 of their papers we have counts for

collaborators

14 papers

math.NT2021

Iterated monodromy groups of rational functions and periodic points over finite fields

Andrew Bridy, Rafe Jones, Gregory Kelsey +1

Let $q$ be a prime power and $ϕ$ a rational function with coefficients in a finite field $F_{q}$ . For $n \geq 1$ , each element of $\mathbb{P}^1(\F_{q^n})$ is either periodic…

math.NT2019★ 5 cited

A question for iterated Galois groups in arithmetic dynamics

Andrew Bridy, John R. Doyle, Dragos Ghioca +2

We formulate a general question regarding the size of the iterated Galois groups associated to an algebraic dynamical system and then we discuss some special cases of our question.

math.NT2019

The Arakelov-Zhang pairing and Julia sets

Andrew Bridy, Matt Larson

The Arakelov-Zhang pairing $⟨ ψ, ϕ ⟩$ is a measure of the "dynamical distance" between two rational maps $ψ$ and $ϕ$ defined over a number field $K$ . It is defined in term…

math.NT2018

Finite index theorems for iterated Galois groups of unicritical polynomials

Andrew Bridy, John R. Doyle, Dragos Ghioca +2

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

math.DS2018★ 3 cited

The cycle structure of unicritical polynomials

Andrew Bridy, Derek Garton

A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: for any prime $p$ , reduce its coefficients mod $p$ and consider its action…

math.NT2017

Finite index theorems for iterated Galois groups of cubic polynomials

Andrew Bridy, Thomas J. Tucker

Let $K$ be a number field or a function field. Let $f \in K (x)$ be a rational function of degree $d \geq 2$ , and let $β \in P^{1} (K)$ . For all $n \in N \cup {\infty}$ , th…

math.NT2017

The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations

Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit +1

We consider a natural generalization of the Nagell-Ljunggren equation to the case where the qth power of an integer y, for q >= 2, has a base-b representation that consists of a le…

math.DS2016★ 7 cited

Dynamically distinguishing polynomials

Andrew Bridy, Derek Garton

A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: for any prime $p$ , reduce its coefficients mod $p$ and consider its action…

math.NT2016

ABC implies a Zsigmondy principle for ramification

Andrew Bridy, Thomas Tucker

Let $K$ be a number field or a function field of characteristic 0. If $K$ is a number field, assume the $ab c$ -conjecture for $K$ . We prove a variant of Zsigmondy's theorem for rami…

math.NT2016★ 13 cited

Automatic Sequences and Curves over Finite Fields

Andrew Bridy

We prove that if $y = \sum_{n = 0}^{\infty} a (n) x^{n} \in F_{q} [[x]]$ is an algebraic power series of degree $d$ , height $h$ , and genus $g$ , then the sequence $a$ is genera…

math.NT2015

Finite ramification for preimage fields of postcritically finite morphisms

Andrew Bridy, Patrick Ingram, Rafe Jones +5

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

math.NT2013

The Artin-Mazur Zeta Function of a Dynamically Affine Rational Map in Positive Characteristic

Andrew Bridy

A dynamically affine map is a finite quotient of an affine morphism of an algebraic group. We determine the rationality or transcendence of the Artin-Mazur zeta function of a dynam…

math.NT2012

On the Number of Distinct Functional Graphs of Affine-Linear Transformations over Finite Fields

Eric Bach, Andrew Bridy

We study the number of non-isomorphic functional graphs of affine-linear transformations from (\F_q)^n to itself, and we prove upper and lower bounds on this quantity for n large.…

math.NT2012★ 3 cited

Transcendence of the Artin-Mazur Zeta Function for Polynomial Maps of A^1(F_p)

Andrew Bridy

We study the rationality of the Artin-Mazur zeta function of a dynamical system defined by a polynomial self-map of A^1(k), where k is the algebraic closure of the finite field F_p…