Defining Bernoulli polynomials in $\textbf {Z}/p\textbf {Z}$ (a generic regularity condition)
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- by Andrew Granville and H. S. Shank PDF
- Proc. Amer. Math. Soc. 108 (1990), 637-640 Request permission
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 Voronoiโs congruences.References
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T. Clausen, Lehrsatz aus einer Abhandlung รผber die Bernoullischen Zahlen, Astronom. Nachr. 17 (1840), 351-352.
- L. J. Dickey, H.-H. Kairies, and H. S. Shank, Analogs of Bernoulli polynomials in fields $Z_{p}$, Aequationes Math. 14 (1976), no.ย 3, 401โ404. MR 409344, DOI 10.1007/BF01835988 K. G. C. Von Staudt, Beweis eines Lehrsatzes, die Bernoullischen Zahlen betreffend, J. Reine Angew. Math. 21 (1840), 372-376. G. F. Voronoi, On Bernoulli numbers, Collected works I, 1952, pp. 7-23.
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 637-640
- MSC: Primary 11B68; Secondary 11A15
- DOI: https://doi.org/10.1090/S0002-9939-1990-0998735-9
- MathSciNet review: 998735