Tomokazu Onozuka

activity

20122026

most citedLaurent series expansions of multiple zeta-functions of Euler-Zagier type at integer points

4 citations · 8 across the 23 of their papers we have counts for

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24 papers · 1 filter

math.NT2026

On the distribution of the zeros of the Euler double zeta-function $ζ_{2} (s, s)$

Kohji Matsumoto, Tomokazu Onozuka, Isao Wakabayashi

We investigate the distribution of zeros of the function $ζ_{2} (s, s)$ , namely the function defined by putting $s_{1} = s_{2} = s$ in the Euler double zeta-function $ζ_{2} (s_{1}, s_{2})$ . Our theore…

math.NT2026

Lower-order terms in mean-square formulas for the Euler--Zagier double zeta-function and regularized multiple zeta values

Tomokazu Onozuka

We study the mean square of the Euler--Zagier double zeta-function when the second variable moves vertically. Mean-square formulas in and beyond the region of absolute convergence…

math.NT2025

On the uniform distribution modulo $1$ of zeros and $a$ -points of zeta functions

Hideki Murahara, Tomokazu Onozuka

Fujii gave five sufficient conditions for the uniform distribution modulo $1$ of the sequence $(u f (γ_{n}))$ , where $γ_{n}$ runs over the imaginary parts of the non-trivial zeros of th…

math.NT2025

A note on order estimates of the $q$ -analogue of the Riemann zeta function

Hideki Murahara, Tomokazu Onozuka

At the first step of studying order estimates for the $q$ -analogue of the Riemann zeta function, we estimate bounds for it on vertical lines for a fixed parameter $q$ .

math.NT2023

Asymptotic coefficients of multiple zeta functions at the origin and generalized Gregory coefficients

Toshiki Matsusaka, Hideki Murahara, Tomokazu Onozuka

Due to their singularities, multiple zeta functions behave sensitively at non-positive integer points. In this article, we focus on the asymptotic behavior at the origin $(0,\dots,…

math.NT2023

Multiple zeta-star values for indices of infinite length

Minoru Hirose, Hideki Murahara, Tomokazu Onozuka

In this paper, we consider infinite-length versions of multiple zeta-star values. We give several explicit formulas for the infinite-length versions of multiple zeta-star values. W…

math.NT2023

On the asymptotic behavior of the double zeta function for large negative indices

Minoru Hirose, Hideki Murahara, Tomokazu Onozuka

In this paper, we investigate an asymptotic behavior of the double zeta function of Euler-Zagier type for indices with large negative real parts.

math.NT2022

Integral expressions for Schur multiple zeta values

Minoru Hirose, Hideki Murahara, Tomokazu Onozuka

Nakasuji, Phuksuwan, and Yamasaki defined the Schur multiple zeta values and gave iterated integral expressions of the Schur multiple zeta values of the ribbon type. This paper gen…

math.NT2021

Asymptotic behavior of the Hurwitz-Lerch multiple zeta function at non-positive integer points

Hideki Murahara, Tomokazu Onozuka

We give a result on the asymptotic behavior of the Hurwitz-Lerch multiple zeta functions near non-positive integer points by using the Apostol-Bernoulli polynomials. From this resu…

math.NT2021

On the linear relations among parametrized multiple series

Minoru Hirose, Hideki Murahara, Tomokazu Onozuka

Parametrized multiple series are generalizations of the multiple zeta values introduced by Igarashi. In this work, we completely determine all the linear relations among these para…

math.NT2020

Connectors of the Ohno relation for parametrized multiple zeta series

Hideki Murahara, Tomokazu Onozuka

The Ohno relation is a well known relation in the theory of multiple zeta values. Recently, Seki and Yamamoto introduced a connector method and gave its succinct proof. On the othe…

math.NT2020

Analytic properties of Ohno function

Ken Kamano, Tomokazu Onozuka

Ohno's relation is a well-known relation on the field of the multiple zeta values and has an interpolation to complex function. In this paper, we call its complex function Ohno fun…

math.NT2020

Cyclic relation for multiple zeta functions

Hideki Murahara, Tomokazu Onozuka

The cyclic relation obtained in a study by Hirose, Murakami, and the first-named author, is a wide class of relations, which includes the well-known cyclic sum formula for multiple…

math.NT2020

On the $a$ -points of symmetric sum of multiple zeta function

Hideki Murahara, Tomokazu Onozuka

In this paper, we present some results on the $a$ -points of the symmetric sum of the Euler-Zagier multiple zeta function. Our first three results are for the $a$ -points free region…

math.NT2019

Linear relations of Ohno sums of multiple zeta values

Minoru Hirose, Hideki Murahara, Tomokazu Onozuka +1

Ohno's relation is a well-known family of relations among multiple zeta values, which can naturally be regarded as a type of duality for a certain power series which we call an Ohn…

math.NT2018

Zeros of a polynomial of $ζ^{(j)} (s)$

Tomokazu Onozuka

We give results on zeros of a polynomial of $ζ (s), ζ^{'} (s), \dots, ζ^{(k)} (s)$ . First, we give a zero free region and prove that there exist zeros corresponding to the trivial zeros of…

math.NT2018

Bowman-Bradley type theorem for finite multiple zeta values in $A_{2}$

Hideki Murahara, Tomokazu Onozuka, Shin-ichiro Seki

Bowman and Bradley obtained a remarkable formula among multiple zeta values. The formula states that the sum of multiple zeta values for indices which consist of the shuffle of two…

math.NT2018

Derivation relation for finite multiple zeta values in $A$

Hideki Murahara, Tomokazu Onozuka

Ihara, Kaneko, and Zagier proved the derivation relation for multiple zeta values. The first named author obtained its counterpart for finite multiple zeta values in $A$ .…

math.NT2018

An interpolation of Ohno's relation to complex functions

Minoru Hirose, Hideki Murahara, Tomokazu Onozuka

Ohno's relation is a well known formula among multiple zeta values. In this paper, we present its interpolation to complex functions.

math.NT2018★ 3 cited

Sum formula for multiple zeta function

Minoru Hirose, Hideki Murahara, Tomokazu Onozuka

The sum formula is a well known relation in the field of the multiple zeta values. In this paper, we present its generalization for the Euler-Zagier multiple zeta function.

math.NT2016

On the $a$ -points of the derivatives of the Riemann zeta function

Tomokazu Onozuka

We prove three results on the $a$ -points of the derivatives of the Riemann zeta function. The first result is a formula of the Riemann-von Mangoldt type; we estimate the number of…

math.NT2016

The multiple Dirichlet product and the multiple Dirichlet series

Tomokazu Onozuka

First, we define the multiple Dirichlet product and study the properties of it. From those properties, we obtain a zero-free region of a multiple Dirichlet series and a multiple Di…

math.NT2016★ 4 cited

Laurent series expansions of multiple zeta-functions of Euler-Zagier type at integer points

Kohji Matsumoto, Tomokazu Onozuka, Isao Wakabayashi

We give explicit expressions (or at least an algorithm of obtaining such expressions) of the coefficients of the Laurent series expansions of the Euler-Zagier multiple zeta-functio…

math.NT2012★ 1 cited

Analytic continuation of multiple zeta-functions and the asymptotic behavior at non-positive integers

Tomokazu Onozuka

We prove two theorems. Theorem 1 gives the meromorphic continuation of the multiple zeta function to the whole space. In Theorem 2, we prove asymptotic behavior near the non-positi…

On the distribution of the zeros of the Euler double zeta-function ζ2​(s,s)

Lower-order terms in mean-square formulas for the Euler--Zagier double zeta-function and regularized multiple zeta values

On the uniform distribution modulo 1 of zeros and a-points of zeta functions

A note on order estimates of the q-analogue of the Riemann zeta function

Asymptotic coefficients of multiple zeta functions at the origin and generalized Gregory coefficients

Multiple zeta-star values for indices of infinite length

On the asymptotic behavior of the double zeta function for large negative indices

Integral expressions for Schur multiple zeta values

Asymptotic behavior of the Hurwitz-Lerch multiple zeta function at non-positive integer points

On the linear relations among parametrized multiple series

Connectors of the Ohno relation for parametrized multiple zeta series

Analytic properties of Ohno function

Cyclic relation for multiple zeta functions

On the a-points of symmetric sum of multiple zeta function

Linear relations of Ohno sums of multiple zeta values

Zeros of a polynomial of ζ(j)(s)

Bowman-Bradley type theorem for finite multiple zeta values in A2​

Derivation relation for finite multiple zeta values in A

An interpolation of Ohno's relation to complex functions

Sum formula for multiple zeta function

On the a-points of the derivatives of the Riemann zeta function

The multiple Dirichlet product and the multiple Dirichlet series

Laurent series expansions of multiple zeta-functions of Euler-Zagier type at integer points

Analytic continuation of multiple zeta-functions and the asymptotic behavior at non-positive integers

On the distribution of the zeros of the Euler double zeta-function $ζ_{2} (s, s)$

On the uniform distribution modulo $1$ of zeros and $a$ -points of zeta functions

A note on order estimates of the $q$ -analogue of the Riemann zeta function

On the $a$ -points of symmetric sum of multiple zeta function

Zeros of a polynomial of $ζ^{(j)} (s)$

Bowman-Bradley type theorem for finite multiple zeta values in $A_{2}$

Derivation relation for finite multiple zeta values in $A$

On the $a$ -points of the derivatives of the Riemann zeta function