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Defining Bernoulli polynomials in  (a generic regularity condition)
Authors:
Andrew Granville and H. S. Shank
Journal:
Proc. Amer. Math. Soc. 108 (1990), 637-640
MSC:
Primary 11B68; Secondary 11A15
MathSciNet review:
998735
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Abstract: We consider the problem of whether Bernoulli polynomials are uniquely defined by certain interpolation equations. This leads to an interesting characterization of regular primes, a new insight into the  -divisibility of Fermat quotients, and a generalization of Voronoi's congruences.
- [1]
T. Clausen, Lehrsatz aus einer Abhandlung über die Bernoullischen Zahlen, Astronom. Nachr. 17 (1840), 351-352.
- [2]
L.
J. Dickey, H.-H.
Kairies, and H.
S. Shank, Analogs of Bernoulli polynomials in fields
𝑍_{𝑝}, Aequationes Math. 14 (1976),
no. 3, 401–404. MR 0409344
(53 #13103)
- [3]
K. G. C. Von Staudt, Beweis eines Lehrsatzes, die Bernoullischen Zahlen betreffend, J. Reine Angew. Math. 21 (1840), 372-376.
- [4]
G. F. Voronoi, On Bernoulli numbers, Collected works I, 1952, pp. 7-23.
- [1]
- T. Clausen, Lehrsatz aus einer Abhandlung über die Bernoullischen Zahlen, Astronom. Nachr. 17 (1840), 351-352.
- [2]
- L. J. Dickey, H.-H. Kairies and H. S. Shank, Analogs of Bernoulli polynomials in fields
 , Aequationes Math. 14 (1976), 401-404. MR 0409344 (53:13103)
- [3]
- K. G. C. Von Staudt, Beweis eines Lehrsatzes, die Bernoullischen Zahlen betreffend, J. Reine Angew. Math. 21 (1840), 372-376.
- [4]
- G. F. Voronoi, On Bernoulli numbers, Collected works I, 1952, pp. 7-23.
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DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-0998735-9
PII:
S 0002-9939(1990)0998735-9
Article copyright:
© Copyright 1990 American Mathematical Society
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