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.
Par le biais des séries logarithmiques multiples, nous définissons l'analogue en plusieurs variables des nombres de Bernoulli. Nous démontrons une formule explicite ainsi qu'un théorème de dualité pour ces nombres. Nous donnons aussi un théorème de type von Staudt et une nouvelle preuve d'un théorème de Vandiver.
@article{JTNB_1997__9_1_221_0, author = {Kaneko, Masanobu}, title = {Poly-Bernoulli numbers}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {221--228}, publisher = {Universit\'e Bordeaux I}, volume = {9}, number = {1}, year = {1997}, mrnumber = {1469669}, zbl = {0887.11011}, language = {en}, url = {http://www.numdam.org/item/JTNB_1997__9_1_221_0/} }
Kaneko, Masanobu. Poly-Bernoulli numbers. Journal de théorie des nombres de Bordeaux, Volume 9 (1997) no. 1, pp. 221-228. http://www.numdam.org/item/JTNB_1997__9_1_221_0/
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