4 citations · 10 across the 4 of their papers we have counts for
8 papers
Index divisibility in the orbit of 0 for integral polynomials
T. Alden Gassert, Michael T. Urbanski
Let $f(x) \in \bbz[x]$ and consider the index divisibility set $D = \{n \in \bbn : n \mid f^n(0)\}$. We present a number of properties of in the case that $(f^n(0))_{n=1}^\inft…
A family of monogenic quartic fields arising from elliptic curves
T. Alden Gassert, Hanson Smith, Katherine E. Stange
We consider partial torsion fields (fields generated by a root of a division polynomial) for elliptic curves. By analysing the reduction properties of elliptic curves, and applying…
Characterizations of numerical semigroup complements via Apéry sets
T. Alden Gassert, Caleb McKinley Shor
In this paper, we generalize the work of Tuenter to give an identity which completely characterizes the complement of a numerical semigroup in terms of its Apéry sets. Using this r…
On Sylvester sums of compound sequence semigroup complements
Thomas A. Gassert, Caleb M. Shor
In this paper, we consider the set of natural numbers which are not in the numerical semigroup generated by a compound sequence . We generalize a result of Tuen…
Index Divisibility in Dynamical Sequences and Cyclic Orbits Modulo
Annie S. Chen, T. Alden Gassert, Katherine E. Stange
Let be an integral polynomial of degree at least 2, and consider the sequence , which is the orbit of under iteration by . Let $D_{d,…
Discriminants of simplest 3^n-tic extensions
T. Alden Gassert
Let be a positive integer, a primitive -th root of unity, and a number field containing but not . In a recent paper, Chonol…
Discriminants of Chebyshev Radical Extensions
Thomas Alden Gassert
Let t be any integer and fix an odd prime ell. Let Phi(x) = T_ell^n(x)-t denote the n-fold composition of the Chebyshev polynomial of degree ell shifted by t. If this polynomial is…
Chebyshev Action on Finite Fields
T. Alden Gassert
Given a polynomial f and a finite field F one can construct a directed graph where the vertices are the values in the finite field, and emanating from each vertex is an edge joinin…