Kummer congruence for the Bernoulli numbers of higher order
type: Item
instance of: scholarly article
title: Kummer congruence for the Bernoulli numbers of higher order
zbMATH Open document ID: 1051.11016
DOI: 10.1016/S0096-3003(03)00314-X
author: Taekyun Kim
author: Dal-Won Park
author: L. C. Jang
published in: Applied Mathematics and Computation
publication date: 2004-08-06T00:00:00Z
review text: The higher order generalized Bernoulli numbers and their \(q\)-analogs were introduced by \textit{T. Kim} and \textit{S. Rim} [Indian J. Pure Appl. Math. 32, No. 10, 1565--1570 (2001; Zbl 1042.11011)], and also by \textit{Y. Jang} and \textit{D. S. Kim} [Appl. Math. Comput. 137, No. 2--3, 387--398 (2003; Zbl 1050.11019)]. In the present paper, Kummer type congruences for these numbers are proved. The technique is based on the Volkenborn non-Archimedean integration theory.
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11S80
zbMATH DE Number: 2081711
zbMATH Keywords: Bernoulli numbers of higher order
zbMATH Keywords: Kummer congruence
zbMATH Keywords: Volkenborn integral
MaRDI profile type: Publication
cites work: On higher order generalized Bernoulli numbers.
cites work: On a multidimensional Volkenborn integral and higher order Bernoulli numbers
cites work: Q3377563
cites work: Sums of products of \(q\)-Bernoulli numbers
cites work: Q3377569
cites work: Generalized Carlitz's \(q\)-Bernoulli numbers in the \(p\)-adic number field
cites work: A note onq-multiple zeta functions
cites work: A note on the values of \(p\)-adic \(q\)-\(L\)-functions.
full work available at URL: s0096-3003(03)00314-x
OpenAlex ID: W2064256906
description: scientific article; zbMATH DE number 2081711