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Polynomials Irreducible by Eisenstein's Criterion

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Abstract.

We compute the probability for a monic univariate integer polynomial to be irreducible by Eisenstein's Criterion. In particular, it follows that less than 1% of the polynomials with at least seven non-zero coefficients are irreducible by Eisenstein.

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Authors and Affiliations

  1. Dept. of Mathematics and Informatics, Vilnius University, Naugarduko 24, 2600, Vilnius, Lithuania

    Artūras Dubickas

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  1. Artūras Dubickas
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Correspondence to Artūras Dubickas.

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Keywords: Irreducible polynomial, Eisenstein's Criterion.

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Dubickas, A. Polynomials Irreducible by Eisenstein's Criterion. AAECC 14, 127–132 (2003). https://doi.org/10.1007/s00200-003-0131-7

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  • DOI: https://doi.org/10.1007/s00200-003-0131-7

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