Kummer congruence for the Bernoulli numbers of higher order
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.
scientific article; zbMATH DE number 2081711