2021/10/04 by Ciprian Mircea Bonciocat, Bonciocat, Ciprian Mircea, Nicolae Ciprian Bonciocat +1
Mathematics · #11C08 #11R09 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11C08 #msc:11R09
paper · pdf · doi:10.48550/arxiv.2110.01327
20 pages, 2 figures
arxiv created 2021/10/04 · arxiv updated 2021/10/05
For a real polynomial f we present explicit zero-free angular sectors in the complex plane, symmetric with respect to the real axis, with angles depending only on the degree of f, and vertices expressed in terms of the coefficients of f. We also describe zero-free lens-shaped regions for f that are associated to the zero-free sectors of the reciprocal of f. As an application, we use these zero-free regions to obtain irreducibility criteria for polynomials with integer coefficients that take a prime or a prime power value.