On the factorization of lacunary polynomials
Volume 210 / 2023
Abstract
This paper addresses the factorization of polynomials of the form where r is a fixed positive integer and the f_{j}(x) are fixed polynomials in \mathbb Z[x] for 0 \le j \le r. We provide an efficient method for showing that for n sufficiently large and reasonable conditions on the f_{j}(x), the non-reciprocal part of F(x) is either 1 or irreducible. We illustrate the approach with a few examples, including two examples that arise from trace fields of hyperbolic 3-manifolds.