On the irreducibility of the non-reciprocal part of polynomials of the form $f(x) x^n + g(x)$
Volume 196 / 2020
Acta Arithmetica 196 (2020), 187-201
MSC: Primary 11R09; Secondary 12E05, 11C08, 13P05.
DOI: 10.4064/aa190907-11-2
Published online: 31 August 2020
Abstract
A recent paper of Sawin, Shusterman and Stoll introduces the notion of robust pairs of polynomials in $\mathbb Z[x]$ and shows that under a condition of robustness the polynomial $f(x) x^{n} + g(x)$ has an irreducible non-reciprocal part provided $n$ is larger than an explicit bound depending only on $f(x)$ and $g(x)$. We establish an improved lower bound.
