Poly-Bernoulli numbers

Masanobu Kaneko

Journal de théorie des nombres de Bordeaux (1997)

  • Volume: 9, Issue: 1, page 221-228
  • ISSN: 1246-7405

Abstract

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By using polylogarithm series, we define “poly-Bernoulli numbers” which generalize classical Bernoulli numbers. We derive an explicit formula and a duality theorem for these numbers, together with a von Staudt-type theorem for di-Bernoulli numbers and another proof of a theorem of Vandiver.

How to cite

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Kaneko, Masanobu. "Poly-Bernoulli numbers." Journal de théorie des nombres de Bordeaux 9.1 (1997): 221-228. <http://eudml.org/doc/247996>.

@article{Kaneko1997,
abstract = {By using polylogarithm series, we define “poly-Bernoulli numbers” which generalize classical Bernoulli numbers. We derive an explicit formula and a duality theorem for these numbers, together with a von Staudt-type theorem for di-Bernoulli numbers and another proof of a theorem of Vandiver.},
author = {Kaneko, Masanobu},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {poly-Bernoulli numbers; Stirling numbers of the second kind; von Staudt-type theorem; theorem of Vandiver; congruences},
language = {eng},
number = {1},
pages = {221-228},
publisher = {Université Bordeaux I},
title = {Poly-Bernoulli numbers},
url = {http://eudml.org/doc/247996},
volume = {9},
year = {1997},
}

TY - JOUR
AU - Kaneko, Masanobu
TI - Poly-Bernoulli numbers
JO - Journal de théorie des nombres de Bordeaux
PY - 1997
PB - Université Bordeaux I
VL - 9
IS - 1
SP - 221
EP - 228
AB - By using polylogarithm series, we define “poly-Bernoulli numbers” which generalize classical Bernoulli numbers. We derive an explicit formula and a duality theorem for these numbers, together with a von Staudt-type theorem for di-Bernoulli numbers and another proof of a theorem of Vandiver.
LA - eng
KW - poly-Bernoulli numbers; Stirling numbers of the second kind; von Staudt-type theorem; theorem of Vandiver; congruences
UR - http://eudml.org/doc/247996
ER -

References

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  1. [1] Gould, H.W.: Explicit formulas for Bernoulli numbers, Amer. Math. Monthly79 (1972), 44-51. Zbl0227.10010MR306102
  2. [2] Ireland, K. and Rosen, M.: A Classical Introduction to Modern Number Theory, second edition. Springer GTM84 (1990) Zbl0712.11001MR1070716
  3. [3] Jordan, Charles:Calculus of Finite Differences, Chelsea Publ. Co., New York, (1950) Zbl0041.05401MR183987
  4. [4] Vandiver, H.S.: On developments in an arithmetic theory of the Bernoulli and allied numbers, Scripta Math.25 (1961), 273-303 Zbl0100.26901MR142497

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