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arXiv · 2409.18404

On congruence properties of poly-Bernoulli numbers with negative upper-indices

Yasuo Ohno·Mika Sakata
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Abstract

For any integer $k$, M.Kaneko defined $k$-th poly-Bernoulli numbers as a kind of generalization of classical Bernoulli numbers using $k$-th polylogarithm. In case when $k$ is positive, $k$-th poly-Bernoulli numbers is a sequence of rational numbers as same as classical Bernoulli numbers. On the other hand, in case when $k$ is negative, it is a sequence of positive integers, and many combinatoric and number theoretic properties has been investigated. In the present paper, the negative case is treated, and their congruence and $p$-adic properties are discussed. Beside of them, application of the results to obtain a congruence property for the number of lonesum matrices is also mentioned.

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Yasuo Ohno, Mika Sakata. 2024-09-27. On congruence properties of poly-Bernoulli numbers with negative upper-indices. https://arxiv.org/abs/2409.18404

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