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The distribution of absolutely irreducible polynomials in several indeterminates


Author: M. L. Fredman
Journal: Proc. Amer. Math. Soc. 31 (1972), 387-390
DOI: https://doi.org/10.1090/S0002-9939-1972-0286779-3
MathSciNet review: 0286779
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Abstract | References | Additional Information

Abstract: Asymptotic formulas are derived for the distribution of absolutely irreducible polynomials in two indeterminates over finite fields. A pair of inversion formulas is presented which yield exact formulas relating the distributions of irreducible and absolutely irreducible polynomials.


References [Enhancements On Off] (What's this?)

  • [1] L. Carlitz, The distribution of irreducible polynomials in several indeterminates, Illinois J. Math. 7 (1963), 371-375. MR 27 #3627. MR 0153665 (27:3627)
  • [2] -, The distribution of irreducible polynomials in several indeterminates. II, Canad. J. Math. 17 (1965), 261-266. MR 30 #3088. MR 0172872 (30:3088)
  • [3] Stephen D. Cohen, The distribution of irreducible polynomials in several indeterminates over a finite field, Proc. Edinburgh Math. Soc. (2) 16 (1968/69), 1-17. MR 38 #138. MR 0231810 (38:138)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0286779-3
Keywords: Irreducible polynomial, absolutely irreducible, several indeterminates, finite fields, inversion formulas, distributions
Article copyright: © Copyright 1972 American Mathematical Society

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