arXiv subjects

Mika Sakata

Publications and source records attributed to Mika Sakata.

5 recordsLinked to original sources

arXiv2024

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

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.

math.NT↗

arXiv2023

Multiple zeta values and Euler's reflection formula for the gamma function

In this paper, we give a purely algebraic proof of an identity coming directly from Euler's reflection formula for the gamma function. Our proof uses Hoffman's harmonic algebra and some binomial identities.

math.NT↗

arXiv2022

Multi-indexed poly-Bernoulli numbers

As properties of poly-Bernoulli numbers, a number of formulas such as the duality formula, explicit formula using the Stirling numbers of the second kind and periodicity for negative upper-index have been established. For the multi-indexed poly-Bernoulli numbers generalized by Kaneko-Tsumura, among such properties only the duality formula was obtained. In this paper, we restrict the double-indexed poly-Bernoulli numbers and show the explicit formula using the Stirling numbers of the second kind and periodicity for negative upper-index for them. Further, we define the variant of multiple-indexed poly-Bernoulli numbers using the star-version of multiple-indexed logarithms and obtain the relation between this kind of double and triple-indexed poly-Bernoulli numbers with multi-indexed poly-Bernoulli numbers ahead.

math.NT↗

arXiv2017

On multiple zeta values and finite multiple zeta values of maximal height

An explicit formula for the height-one multiple zeta values was proved by Kaneko and the second author. We give an alternative proof of this result and its generalization. We also prove its counterpart for the finite multiple zeta values.

math.NT↗

arXiv2015

On multiple zeta values of extremal height

We give three identities involving multiple zeta values of height one and of maximal height; an explicit formula for the height-one multiple zeta values, a regularized sum formula, and a sum formula for the multiple zeta values of maximal height.

math.NT↗