T. N. Shorey’s Influence in the Theory of Irreducible Polynomials

The idea of looking at the prime factorization of the coefficients of a polynomial in Z[x] in order to establish its irreducibility (over Q) goes back to the classical Schönemann-Eisenstein criterion first derived in [29] and [6] in the middle of the 19th century. At the beginning of the 20th century, G. Dumas [5], again making use of primes that divide the coefficients of a polynomial, introduced the idea of using Newton polygons which allowed for variations and strengthening of the Schönemann-Eisenstein criterion. In a series of papers, I. Schur [30, 31, 32, 33] obtained irreducibility results for polynomials f(x) associated with generalized Laguerre polynomials