Greg Knapp

collaborators

3 papers

math.NT2024

Upper Bounds on Polynomial Root Separation

Greg Knapp, Chi Hoi Yip

In this paper, we consider the relationship between the Mahler measure of a polynomial and its separation. In 1964, Mahler proved that if $f (x) \in Z [x]$ is separable of d…

math.NT2024

On Certain Polytopes Associated to Products of Algebraic Integer Conjugates

Seda Albayrak, Samprit Ghosh, Greg Knapp +1

Let $d > k$ be positive integers. Motivated by an earlier result of Bugeaud and Nguyen, we let $E_{k, d}$ be the set of $(c_{1}, \dots, c_{k}) \in R_{\geq 0}^{k}$ such that $\vertα_0\…

math.NT2022

The Number of Solutions to the Trinomial Thue Equation

Greg Knapp

In this paper, we study the number of integer pair solutions to the equation $∣ F (x, y) ∣ = 1$ where $F (x, y) \in Z [x, y]$ is an irreducible (over $Z$ ) binary form wit…