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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Defining Bernoulli polynomials in $ {\bf Z}/p{\bf Z}$ (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 | References | Similar Articles | Additional Information

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 $ p$-divisibility of Fermat quotients, and a generalization of Voronoi's congruences.


References [Enhancements On Off] (What's this?)

  • [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.

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Additional Information

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