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Irreducibility of polynomials modulo p via Newton polytopes
Institution:a Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA
b Faculdade de Matemática, PUCRS, Av. Ipiranga, 6681, Porto Alegre, RS 90619-900, Brazil
Abstract:Ostrowski established in 1919 that an absolutely irreducible integral polynomial remains absolutely irreducible modulo all sufficiently large prime numbers. We obtain a new lower bound for the size of such primes in terms of the number of integral points in the Newton polytope of the polynomial, significantly improving previous estimates for sparse polynomials.
Keywords:Primary: 12E05  Secondary: 11R09  52B20
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