On Congruence Properties of Poly-Bernoulli Numbers with Negative Upper Indices
Abstract
Kaneko defined poly-Bernoulli numbers as a kind of generalization of classical Bernoulli numbers using the polylogarithm. When the upper index is a positive integer, the poly-Bernoulli numbers are a sequence of rational numbers that are analogous to the classical Bernoulli numbers. On the other hand, when the upper index is a negative integer, they are a sequence of positive integers, and many combinatorial and number theoretic properties have been investigated. In the present paper, the negative case is treated, and their congruence and p-adic properties are discussed. In addition, the application of the results to obtain congruence properties for the number of lonesum matrices are also mentioned.
Fields of Study & Subjects
Advanced Mathematical Identities
Mathematical functions and polynomials
Analytic Number Theory Research
Publication details
- Journal / source
- Tokyo Journal of Mathematics
- Publisher
- Tokyo Journal of Mathematics
- Volume
- 49
- Issue
- 1
- Pages
- 151–160
- Publication date
- 1 June 2026
- Language
- EN