Emerald Stacy

activity

20192024

collaborators

3 papers

math.DS2024

On a Slice of the Cubic 2-adic Mandelbrot Set

Jacqueline Anderson, Emerald Stacy, Bella Tobin

Consider the one-parameter family of cubic polynomials defined by $f_{t} (z) = - \frac{3}{2} t (- 2 z^{3} + 3 z^{2}) + 1, t \in C_{2}$ . This family corresponds to a slice of the parameter space…

math.NT2020

Totally p-adic Numbers of Degree 3

Emerald Stacy

The height of an algebraic number $α$ is a measure of how arithmetically complicated $α$ is. We say $α$ is totally $p$ -adic if the minimal polynomial of $α$ splits completely over…

math.NT2019

A dynamical construction of small totally $p$ -adic algebraic numbers

Clayton Petsche, Emerald Stacy

We give a dynamical construction of an infinite sequence of distinct totally $p$ -adic algebraic numbers whose Weil heights tend to the limit $\frac{l o g p}{p - 1}$ , thus giving a new…

On a Slice of the Cubic 2-adic Mandelbrot Set

Totally p-adic Numbers of Degree 3

A dynamical construction of small totally p-adic algebraic numbers

A dynamical construction of small totally $p$ -adic algebraic numbers