# On the degrees of irreducible factors of higher order Bernoulli polynomials

Acta Arithmetica (1992)

- Volume: 62, Issue: 4, page 329-342
- ISSN: 0065-1036

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topArnold Adelberg. "On the degrees of irreducible factors of higher order Bernoulli polynomials." Acta Arithmetica 62.4 (1992): 329-342. <http://eudml.org/doc/206497>.

@article{ArnoldAdelberg1992,

author = {Arnold Adelberg},

journal = {Acta Arithmetica},

keywords = {-Eisenstein behavior; Bernoulli polynomials; irreducibility},

language = {eng},

number = {4},

pages = {329-342},

title = {On the degrees of irreducible factors of higher order Bernoulli polynomials},

url = {http://eudml.org/doc/206497},

volume = {62},

year = {1992},

}

TY - JOUR

AU - Arnold Adelberg

TI - On the degrees of irreducible factors of higher order Bernoulli polynomials

JO - Acta Arithmetica

PY - 1992

VL - 62

IS - 4

SP - 329

EP - 342

LA - eng

KW - -Eisenstein behavior; Bernoulli polynomials; irreducibility

UR - http://eudml.org/doc/206497

ER -

## References

top- [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. Zbl0771.11014
- [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. Zbl0047.25401
- [5] L. Carlitz, The irreducibility of the Bernoulli polynomial ${B}_{14}\left(x\right)$, Math. Comp. 19 (1965), 667-670. Zbl0135.01703
- [6] N. Kimura, On the degree of an irreducible factor of the Bernoulli polynomials, Acta Arith. 50 (1988), 243-249. Zbl0655.10008
- [7] P. J. McCarthy, Irreducibility of certain Bernoulli polynomials, Amer. Math. Monthly 68 (1961), 352-353. Zbl0098.24803
- [8] P. J. McCarthy, Some irreducibility theorems for Bernoulli polynomials of higher order, Duke Math. J. 27 (1960), 313-318. Zbl0178.37302
- [9] P. J. McCarthy, Irreducibility of Bernoulli polynomials of higher order, Canad. J. Math. 14 (1962), 565-567. Zbl0118.26001
- [10] I. Niven, H. Zuckerman and H. Montgomery, An Introduction to the Theory of Numbers, 5th ed., Wiley, 1991. Zbl0742.11001
- [11] N. E. Nörlund, Differenzenrechnung, Springer, 1924.
- [12] S. Roman, The Umbral Calculus, Academic Press, 1984. Zbl0536.33001

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