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Irreducibility of Bernoulli Polynomials of Higher Order
Published online by Cambridge University Press: 20 November 2018
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The Bernoulli polynomials of order k, where k is a positive integer, are defined by
Bm(k)(x) is a polynomial of degree m with rational coefficients, and the constant term of Bm(k)(x) is the mth Bernoulli number of order k, Bm(k). In a previous paper (3) we obtained some conditions, in terms of k and m, which imply that Bm(k)(x) is irreducible (all references to irreducibility will be with respect to the field of rational numbers). In particular, we obtained the following two results.
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- Copyright © Canadian Mathematical Society 1962
References
1.
Carlitz, L., Note on irreducibility of the Bernoulli and Euler polynomials, Duke Math. J., 19 (1952), 475–481.Google Scholar
2.
Carlitz, L., A note on Bernoulli numbers of higher order, Scripta Math., 22 (1956), 217–221.Google Scholar
3.
McCarthy, P. J., Some irreducibility theorems for Bernoulli polynomials of higher order, Duke Math. J., 27 (1960), 313–318.Google Scholar
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