Trevor Hyde

activity

20102026

most citedPolynomial splitting measures and cohomology of the pure braid group

6 citations · 10 across the 17 of their papers we have counts for

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12 papers · 1 filter

math.NT2026

Rational orbits under correspondences

Trevor Hyde

Consider an algebraic function like $F (x) = x^{3} - 1$ . If $p \in Q$ is a rational number, how many iterates of $p$ under $F$ can also be rational? The dynamics of al…

math.NT2021

Dynatomic polynomials, necklace operators, and universal relations for dynamical units

John R. Doyle, Paul Fili, Trevor Hyde

Given a generic polynomial $f (x)$ , the generalized dynatomic polynomial $Φ_{f, c, d} (x)$ vanishes at precisely those $α$ such that $f^{c} (α)$ has period exactly $d$ under iteration of…

math.NT2021

Density of Periodic Points for Lattès maps over Finite Fields

Zoë Bell, Jasmine Camero, Karina Cho +5

Let $L_{d}$ be the Lattès map associated to the multiplication-by- $d$ endomorphism of an elliptic curve $E$ defined over a finite field $F_{q}$ . We determine the density $δ(L_…

math.NT2018★ 1 cited

Normal elements in finite fields

Trevor Hyde

We give a simple derivation of the formula for the number of normal elements in an extension of finite fields. Our proof is based on the fact that units in the Galois group ring of…

math.NT2018

Liminal reciprocity and factorization statistics

Trevor Hyde

Let $M_{d, n} (q)$ denote the number of monic irreducible polynomials in $F_{q} [x_{1}, x_{2}, \dots, x_{n}]$ of degree $d$ . We show that for a fixed degree $d$ , the sequence $M_{d…

math.NT2017

Factorization statistics and the twisted Grothendieck-Lefschetz formula

Trevor Hyde

We announce recent results on a connection between factorization statistics of polynomials over a finite field and the structure of the cohomology of configurations in $\mathbb{R}^…

math.NT2017

Collusions in Teichmüller expansions

Trevor Hyde

If $p \subseteq Z [ζ]$ is a prime ideal over $p$ in the $(p^{d} - 1)$ th cyclotomic extension of $Z$ , then every element $α$ of the completion $\mathbb{Z}[…

math.NT2015

Gauss' hidden menagerie: from cyclotomy to supercharacters

Stephan Ramon Garcia, Trevor Hyde, Bob Lutz

Gaussian periods, when viewed appropriately, exhibit a dazzling and eclectic host of visual qualities. This brief survey reviews the historical context and summarizes our current k…

math.NT2013

Small dynamical heights for quadratic polynomials and rational functions

Robert L. Benedetto, Ruqian Chen, Trevor Hyde +2

Let $f \in Q (z)$ be a polynomial or rational function of degree 2. A special case of Morton and Silverman's Dynamical Uniform Boundedness Conjecture states that the number of ratio…

math.NT2012

A Wallis Product on Clovers

Trevor Hyde

We prove a generalization of the Wallis product for a sequence of real numbers related to arc lengths of clover curves. Our proof generalizes a common argument given for the origin…

math.NT2012

The Galois theory of the lemniscate

David A. Cox, Trevor Hyde

This article studies the Galois groups that arise from division points of the lemniscate. We compute these Galois groups two ways: first, by class field theory, and second, by prov…

math.NT2010

Pre-images of quadratic dynamical systems

Benjamin Hutz, Trevor Hyde, Benjamin Krause

For a quadratic endomorphism of the affine line defined over the rationals we consider the problem of bounding the number of rational points that eventually land at a given constan…