On the degrees of irreducible factors of higher order Bernoulli polynomials

• Autorzy: Arnold Adelberg
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1992
• Tom: 62
• Numer: 4
• Strony: 329-342

Daty

wydano

1992

otrzymano

1991-09-04

poprawiono

1992-06-23

Twórcy

autor

Arnold Adelberg

• Department of Mathematics and Computer Science, Grinnell College, Grinnell, Iowa 50112, U.S.A.

Bibliografia

• [1] A. Adelberg, A finite difference approach to degenerate Bernoulli and Stirling polynomials, Discrete Math., submitted.
• [2] A. Adelberg, Irreducible factors and p-adic poles of higher order Bernoulli polynomials, C. R. Math. Rep. Acad. Sci. Canada 14 (1992), 173-178.
• [3] J. Brillhart, On the Euler and Bernoulli polynomials, J. Reine Angew. Math. 234 (1969), 45-64.
• [4] L. Carlitz, Note on irreducibility of the Bernoulli and Euler polynomials, Duke Math. J. 19 (1952), 475-481.
• [5] L. Carlitz, The irreducibility of the Bernoulli polynomial $B_{14}(x)$, Math. Comp. 19 (1965), 667-670.
• [6] N. Kimura, On the degree of an irreducible factor of the Bernoulli polynomials, Acta Arith. 50 (1988), 243-249.
• [7] P. J. McCarthy, Irreducibility of certain Bernoulli polynomials, Amer. Math. Monthly 68 (1961), 352-353.
• [8] P. J. McCarthy, Some irreducibility theorems for Bernoulli polynomials of higher order, Duke Math. J. 27 (1960), 313-318.
• [9] P. J. McCarthy, Irreducibility of Bernoulli polynomials of higher order, Canad. J. Math. 14 (1962), 565-567.
• [10] I. Niven, H. Zuckerman and H. Montgomery, An Introduction to the Theory of Numbers, 5th ed., Wiley, 1991.
• [11] N. E. Nörlund, Differenzenrechnung, Springer, 1924.
• [12] S. Roman, The Umbral Calculus, Academic Press, 1984.