Irreducibility of polynomials modulo p via Newton polytopes |
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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 |
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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. |
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Keywords: | Primary: 12E05 Secondary: 11R09 52B20 |
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