W. Hindes

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20122025

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14 papers · 1 filter

math.NT2025

Preperiodic integers for $x^{d} + c$ in large degree

John R. Doyle, Wade Hindes

Given a number field $K$ , we completely classify the preperiodic portraits of the maps $x^{d} + c$ where $c \in K$ is an algebraic integer and $d$ is sufficiently large depending on the…

math.NT2025

Prime-powered images and irreducible polynomials in dynamical semigroups

Aristaa Bhardwaj, Adrian Boyer-Paulet, Wade Hindes +2

Let $G = ⟨ x^{d} + c_{1}, \dots, x^{d} + c_{s} ⟩$ be a semigroup generated under composition for some $c_{1}, \dots, c_{s} \in Z$ and some $d \geq 2$ . Then we prove that, outside of an e…

math.NT2025

On the factorization of iterates of $x^{d} + c$ in large degree

Wade Hindes

Let $K$ be a function field of a curve in characteristic zero or a number field over which the $ab c$ -conjecture holds, fix $α \in K$ , and let $f_{d, c} (x) = x^{d} + c$ for some $d \geq 2$ an…

math.NT2022

Dynamical Diophantine Approximation Exponents in Characteristic $p$

Wade Hindes

Let $ϕ (z)$ be a non-isotrivial rational function in one-variable with coefficients in $F_{p} (t)$ and assume that $γ \in P^{1} (F_{p} (t))$ is…

math.NT2020

Orbit counting in polarized dynamical systems

Wade Hindes

We extend recent orbit counts for finitely generated semigroups acting on $P^{N}$ to certain infinitely generated, polarized semigroups acting on projective varieties. We th…

math.NT2020

Counting points of bounded height in monoid orbits

Wade Hindes

Given a set of endomorphisms on $P^{N}$ , we establish an upper bound on the number of points of bounded height in the associated monoid orbits. Moreover, we give a more refi…

Preperiodic integers for xd+c in large degree

Prime-powered images and irreducible polynomials in dynamical semigroups

On the factorization of iterates of xd+c in large degree

Dynamical Diophantine Approximation Exponents in Characteristic p

Orbit counting in polarized dynamical systems

Counting points of bounded height in monoid orbits

Preperiodic integers for $x^{d} + c$ in large degree

On the factorization of iterates of $x^{d} + c$ in large degree

Dynamical Diophantine Approximation Exponents in Characteristic $p$