arXiv subjects

Kyosuke Nishibiro

Publications and source records attributed to Kyosuke Nishibiro.

3 recordsLinked to original sources

arXiv2023

On generalization of duality formulas for the Arakawa-Kaneko type zeta functions

Kaneko and Tsumura introduced the Arakawa-Kaneko type zeta function $η(-k_1,\ldots,-k_r;s_1,\ldots,s_r)$ for non-negative integers $k_1,\ldots,k_r$ and complex variables $s_1,\ldots,s_r$. Recently, Yamamoto showed that, by using the multiple integral expression, $η(u_1,\ldots,u_r;s_1,\ldots,s_r)$ can be extended to an analytic function of 2$r$ variables. Also, he showed that the function $η(u_1,\ldots,u_r;s_1,\ldots,s_r)$ satisfies a duality formula. In this paper, by using the a generalization of non-strict multi-indexed polylogarithm, we define a kind of Arakawa-Kaneko type zeta function, and show that this function satisfies a certain duality formula.

math.NT↗

arXiv2023

On explicit relations for values of Kaneko-Tsumura's $λ$ function

Recently, Kaneko and Tsumura introduced multiple $\widetilde{T}$-values, another kind of poly-Euler numbers and the related Arakawa-Kaneko type zeta function. It is shown that each of them satisfies similar formulas to those of multiple zeta values, poly-Bernoulli numbers and the related Arakawa-Kaneko type zeta function. In this paper, we show some explicit relations for values of Kaneko-Tsumura $λ$ function at positive integers, including the duality type relation.

math.NT↗

arXiv2022

On some properties of polycosecant numbers and polycotangent numbers

Polycosecant numbers and polycotangent numbers are introduced as level two analogues of poly-Bernoulli numbers. It is shown that polycosecant numbers and polycotangent numbers satisfy many formulas similar to those of poly-Bernoulli numbers. However, there is much unknown about polycotangent numbers. For example, the zeta function interpolating them at non-positive integers has not yet been constructed. In this paper, we show some algebraic properties of polycosecant numbers and polycotangent numbers. Also, we generalize duality formulas for polycosecant numbers which essentially include those for polycotangent numbers.

math.NT↗