# Poly-Bernoulli numbers

Journal de théorie des nombres de Bordeaux (1997)

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

## Access Full Article

top## Abstract

top## How to cite

topKaneko, 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

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

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.