Greg Knapp

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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 $\vertÎ±_0…