The distribution of absolutely irreducible polynomials in several indeterminates

Fredman, M. L.

doi:10.1090/S0002-9939-1972-0286779-3

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The distribution of absolutely irreducible polynomials in several indeterminates
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by M. L. Fredman PDF

Proc. Amer. Math. Soc. 31 (1972), 387-390 Request permission

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

L. Carlitz, The distribution of irreducible polynomials in several indeterminates, Illinois J. Math. 7 (1963), 371–375. MR 153665
L. Carlitz, The distribution of irreducible polynomials in several indeterminates. II, Canadian J. Math. 17 (1965), 261–266. MR 172872, DOI 10.4153/CJM-1965-025-1
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 231810, DOI 10.1017/S001309150001213X

Additional Information

Journal: Proc. Amer. Math. Soc. 31 (1972), 387-390
DOI: https://doi.org/10.1090/S0002-9939-1972-0286779-3
MathSciNet review: 0286779