Irreducibility of polynomials with low absolute values
Robert J. Levit · Transactions of the American Mathematical Society · 1968
LEVIT 1. Introduction.We shall be concerned with irreducibility criteria of the following form: An integral polynomial (i.e., polynomial with integral coefficients) Pn(x) of degree n is irreducible over the rational field if there are m distinct integers Xx,x2,..., xmfor which 0< ¡P"(X)| < T(m, n), where T(m, n) is a specified function of m and « only.The first such criterion was given by G. Pólya [4] for m = n.In a comprehensive paper [1], which includes an account of the earlier results, A. Brauer and G. Ehrlich established the highest bounds T(m, ri) to date-namely,