Trevor Hyde

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20122021

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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

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.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…