6 citations · 10 across the 17 of their papers we have counts for
20 papers
The Arithmetic of Semirings Part I: Ideals
Jay Chen, Trevor Hyde, Dorien Laurens +2
We study ideals in the semiring of natural numbers, with a focus on those which are lost when extending from to . This leads to a new perspect…
Rational orbits under correspondences
Trevor Hyde
Consider an algebraic function like . If is a rational number, how many iterates of under can also be rational? The dynamics of al…
Polynomials with many rational preperiodic points
John R. Doyle, Trevor Hyde
In this paper we study two questions related to exceptional behavior of preperiodic points of polynomials in . We show that for all , there exists a polynom…
Dynamical moduli spaces and polynomial endomorphisms of configurations
Talia Blum, John R. Doyle, Trevor Hyde +3
A portrait is a combinatorial model for a discrete dynamical system on a finite set. We study the geometry of portrait moduli spaces, whose points correspond to equivalence classes…
Dynatomic polynomials, necklace operators, and universal relations for dynamical units
John R. Doyle, Paul Fili, Trevor Hyde
Given a generic polynomial , the generalized dynatomic polynomial vanishes at precisely those such that has period exactly under iteration of…
Density of Periodic Points for Lattès maps over Finite Fields
Zoë Bell, Jasmine Camero, Karina Cho +5
Let be the Lattès map associated to the multiplication-by- endomorphism of an elliptic curve defined over a finite field . We determine the density $δ(L_…
Euler characteristic of the space of real multivariate irreducible polynomials
Trevor Hyde
We compute the compactly supported Euler characteristic of the space of degree irreducible polynomials in variables with real coefficients and show that the values are give…
Cyclotomic factors of necklace polynomials
Trevor Hyde
We observe that the necklace polynomials are highly reducible over with many cyclotomic factors. Furthermore, the seque…
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…
Liminal reciprocity and factorization statistics
Trevor Hyde
Let denote the number of monic irreducible polynomials in of degree . We show that for a fixed degree , the sequence $M_{d…
Polynomial factorization statistics and point configurations in
Trevor Hyde
We use generating functions to relate the expected values of polynomial factorization statistics over to the cohomology of ordered configurations in a…
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}^…
Collusions in Teichmüller expansions
Trevor Hyde
If is a prime ideal over in the th cyclotomic extension of , then every element of the completion $\mathbb{Z}[…
Circulant q-Butson Hadamard matrices
Trevor Hyde, Joseph Kraisler
If is a prime power, then a -dimensional \emph{-Butson Hadamard matrix} is a matrix with all entries th roots of unity such that . W…
Polynomial splitting measures and cohomology of the pure braid group
Trevor Hyde, Jeffrey C. Lagarias
We study for each a one-parameter family of complex-valued measures on the symmetric group , which interpolate the probability of a monic, degree , square-free polynomi…
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…
Small dynamical heights for quadratic polynomials and rational functions
Robert L. Benedetto, Ruqian Chen, Trevor Hyde +2
Let 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…
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…
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…
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…