W. Hindes

activity

20122026

most citedDynamical height growth: left, right, and total orbits

6 citations · 15 across the 18 of their papers we have counts for

collaborators

34 papers

math.NT2026

Arithmetic growth in partially commutative semigroups of endomorphisms

Wade Hindes

We establish asymptotics for the degree and height growth rate functions of partially commutative semigroups of endomorphisms of varieties, i.e., semigroups where the only relation…

math.NT2026

Free semigroups of power series

Wade Hindes

Given power series $f_{1}, \dots, f_{r} \in z^{2} K [[z]]$ over a field $K$ , we show that the semigroup $⟨ f_{1}, \dots, f_{r} ⟩$ generated by the $f$ 's under composition is free of rank…

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.NT2024

Unicritical polynomials over $ab c$ -fields: from uniform boundedness to dynamical Galois groups

John R. Doyle, Wade Hindes

Let $K$ be a function field of characteristic $p \geq 0$ or a number field over which the $ab c$ conjecture holds, and let $ϕ (x) = x^{d} + c \in K [x]$ be a unicritical polynomial of degree…

math.NT2023

On the proportion of irreducible polynomials in unicritically generated semigroups

Wade Hindes, Reiyah Jacobs, Benjamin Keller +3

Let $p$ be a prime number and let $S = {x^{p} + c_{1}, \dots, x^{p} + c_{r}}$ be a finite set of unicritical polynomials for some $c_{1}, \dots, c_{r} \in Z$ . Moreover, assume that $S$ contains…

math.NT2023★ 1 cited

Counting points by height in semigroup orbits

Jason P. Bell, Wade Hindes, Xiao Zhong

We improve known estimates for the number of points of bounded height in semigroup orbits of polarized dynamical systems. In particular, we give exact asymptotics for generic semig…

math.NT2023★ 2 cited

The size of semigroup orbits modulo primes

Wade Hindes, Joseph H. Silverman

Let $V$ be a projective variety defined over a number field $K$ , let $S$ be a polarized set of endomorphisms of $V$ all defined over $K$ , and let $P \in V (K)$ . For each prime $\math…

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.NT2022★ 1 cited

Irreducible polynomials in quadratic semigroups

Wade Hindes, Reiyah Jacobs, Peter Ye

We construct many irreducible polynomials within semigroups generated by sets of the form $S = {x^{2} + c_{1}, \dots, x^{2} + c_{s}}$ under composition.

math.NT2021

Galois groups and prime divisors in random quadratic sequences

John R. Doyle, Vivian Olsiewski Healey, Wade Hindes +1

Given a set $S = {x^{2} + c_{1}, \dots, x^{2} + c_{s}}$ defined over a field and an infinite sequence $γ$ of elements of $S$ , one can associate an arboreal representation to $γ$ , generalizing th…

math.NT2021★ 3 cited

Integral points in orbits in characteristic $p$

Alexander Carney, Wade Hindes, Thomas J. Tucker

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 t…

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…

math.NT2020★ 6 cited

Dynamical height growth: left, right, and total orbits

Wade Hindes

Let $S$ be a set of dominant rational self-maps on $P^{N}$ . We study the arithmetic and dynamical degrees of infinite sequences of $S$ obtained by sequentially composing ele…

math.NT2019

Dynamical and arithmetic degrees for random iterations of maps on projective space

Wade Hindes

We show that the dynamical degree of an (i.i.d) random sequence of dominant, rational self-maps on projective space is almost surely constant. We then apply this result to height g…

math.NT2019

Eventually stable quadratic polynomials over $Q$

David DeMark, Wade Hindes, Rafe Jones +3

We study the number of irreducible factors (over $Q$ ) of the $n$ th iterate of a polynomial of the form $f_{r} (x) = x^{2} + r$ for rational $r$ . When the number of such factors…

math.NT2018

Finite orbit points for sets of quadratic polynomials

Wade Hindes

Let $S = {x^{2} + c_{1}, x^{2} + c_{2}, \dots, x^{2} + c_{s}}$ be a set of quadratic polynomials with rational coefficients, and let $P$ be a rational basepoint. We classify the pairs $(S, P)$ for whi…

math.NT2018

Stochastic Canonical Heights

Vivian Olsiewski Healey, Wade Hindes

We construct height functions defined stochastically on projective varieties equipped with endomorphisms, and we prove that these functions satisfy analogs of the usual properties…

math.NT2017

Riccati equations and polynomial dynamics over function fields

Wade Hindes, Rafe Jones

Given a function field $K$ and $ϕ \in K [x]$ , we study two finiteness questions related to iteration of $ϕ$ : whether all but finitely many terms of an orbit of $ϕ$ must possess a pri…

math.NT2017

Galois groups of some iterated polynomials over cyclotomic extensions

Wade Hindes

Let $φ_{p} (z) = (z - 1)^{p} + 2 - ζ_{p}$ , where $ζ_{p} \in Q ˉ$ is a primitive $p$ -th root of unity for some odd prime $p$ . Building on previous work, we show that the $n$ -th iterate $φ…

math.NT2017★ 1 cited

Classifying Galois groups of small iterates via rational points

Wade Hindes

We establish several surjectivity theorems regarding the Galois groups of small iterates of $ϕ_{c} (x) = x^{2} + c$ for $c \in Q$ . To do this, we use explicit techniques from the the…

math.NT2016

Integrality estimates in orbits over function fields

Wade Hindes

We prove a version of Silverman's dynamical integral point theorem for a large class of rational functions defined over global function fields.

Arithmetic growth in partially commutative semigroups of endomorphisms

Free semigroups of power series

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

Unicritical polynomials over abc-fields: from uniform boundedness to dynamical Galois groups

On the proportion of irreducible polynomials in unicritically generated semigroups

Counting points by height in semigroup orbits

The size of semigroup orbits modulo primes

Dynamical Diophantine Approximation Exponents in Characteristic p

Irreducible polynomials in quadratic semigroups

Galois groups and prime divisors in random quadratic sequences

Integral points in orbits in characteristic p

Orbit counting in polarized dynamical systems

Counting points of bounded height in monoid orbits

Dynamical height growth: left, right, and total orbits

Dynamical and arithmetic degrees for random iterations of maps on projective space

Eventually stable quadratic polynomials over Q

Finite orbit points for sets of quadratic polynomials

Stochastic Canonical Heights

Riccati equations and polynomial dynamics over function fields

Galois groups of some iterated polynomials over cyclotomic extensions

Classifying Galois groups of small iterates via rational points

Integrality estimates in orbits over function fields

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

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

Unicritical polynomials over $ab c$ -fields: from uniform boundedness to dynamical Galois groups

Dynamical Diophantine Approximation Exponents in Characteristic $p$

Integral points in orbits in characteristic $p$

Eventually stable quadratic polynomials over $Q$