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Automatic Sequences and Curves over Finite Fields

- Andrew Bridy
- Mathematics
- 27 April 2016

We prove that if $y=\sum_{n=0}^\infty{\bf a}(n)x^n\in\mathbb{F}_q[[x]]$ is an algebraic power series of degree $d$, height $h$, and genus $g$, then the sequence ${\bf a}$ is generated by an automaton… Expand

On the number of distinct functional graphs of affine-linear transformations over finite fields

- E. Bach, Andrew Bridy
- Mathematics
- 15 August 2012

Abstract 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 as n→∞. As a corollary… Expand

FINITE RAMIFICATION FOR PREIMAGE FIELDS OF POSTCRITICALLY FINITE MORPHISMS

- Andrew Bridy, Patrick Ingram, +5 authors J. Silverman
- Mathematics
- 1 November 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}… Expand

Transcendence of the Artin–Mazur zeta function for polynomial maps of $\mathbb A^1(\overline{\mathbb F}_p)$

- Andrew Bridy
- Mathematics
- 2012

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

- Andrew Bridy
- Mathematics
- 21 June 2013

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 dynamically affine… Expand

Dynamically distinguishing polynomials

- Andrew Bridy, D. Garton
- Mathematics
- 29 September 2016

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 on the field… Expand

The Generalized Nagell–Ljunggren Problem: Powers with Repetitive Representations

- Andrew Bridy, R. Oliver, Arlo Shallit, J. Shallit
- Mathematics, Computer Science
- Exp. Math.
- 12 July 2017

TLDR

Finite index theorems for iterated Galois groups of cubic polynomials

- Andrew Bridy, T. Tucker
- Mathematics
- 6 October 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… Expand

Finite index theorems for iterated Galois groups of unicritical polynomials.

- Andrew Bridy, J. Doyle, D. Ghioca, Liang-Chung Hsia, T. Tucker
- Mathematics
- 1 October 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… Expand

Zeta Functions of Polynomial Dynamics on the Algebraic Closure of a Finite Field

- Andrew Bridy
- Mathematics
- 2 February 2012

We study the rationality of the Artin-Mazur zeta function of a dynamical system defined by a polynomial map on the algebraic closure of the finite field F_p. The zeta functions of the maps f(x)=x^m… Expand

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