Kummer-type congruences for multi-poly-Bernoulli numbers

TL;DR

This paper establishes Kummer-type congruences for multi-poly-Bernoulli numbers using $p$-adic distributions, extending classical results for Bernoulli numbers to a broader class.

Contribution

It introduces new Kummer-type congruences for multi-poly-Bernoulli numbers, a generalization of Bernoulli numbers, via $p$-adic distribution methods.

Findings

Proves Kummer-type congruences for multi-poly-Bernoulli numbers.

Extends classical Bernoulli number congruences to a multi-poly setting.

Uses $p$-adic distributions to establish these congruences.

Abstract

The multi-poly-Bernoulli numbers are generalizations of the Bernoulli numbers. In this paper, we will prove Kummer-type congruences for multi-poly-Bernoulli numbers via $p$-adic distributions.