On some bounds for zeros of norm-bounded polynomials (Q1892120)

Let \(P(M, n)\) denote the set of all irreducible polynomials over \(\mathbb{Z}\) of degree at most \(n\) and of norm at most \(M\) and let \(\mathbb{Z}(M, n)\) denote the set of all zeros of polynomials in \(P(M, n)\). The author defines a sufficiently large region that does not contain any zeros in \(\mathbb{Z}(M, n)\) and is easy to analyze. Three norms are considered, that is, 1-norm, 2-norm and \(\infty\)-norm. He describes such regions. Moreover, he calculates the distributions of their zeros by computer and compares them with the regions.