M. Hirose

Interpolated polynomial multiple zeta values of fixed weight, depth, and height

Minoru Hirose, Hideki Murahara, Shingo Saito

We define the interpolated polynomial multiple zeta values as a generalization of all of multiple zeta values, multiple zeta-star values, interpolated multiple zeta values, symmetr…

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.NT2022★ 1 cited

Block shuffle identities for multiple zeta values

Minoru Hirose, Nobuo Sato

In 1998, Borwein, Bradley, Broadhurst and Lisoněk posed two families of conjectural identities among multiple zeta values, later generalized by Charlton using his alternating block…

Colored double zeta values and modular forms of general level

Minoru Hirose

Gangl, Kaneko, and Zagier gave explicit linear relations among double zeta values of odd indices coming from the period polynomials of modular forms for $SL (2, Z)$ . I…

physics.acc-ph2022★ 4 cited

$t$ -adic symmetric multiple zeta values for indices in which $1$ and $3$ appear alternately

Minoru Hirose, Hideki Murahara, Shingo Saito

We consider the symmetric multiple zeta values in $S_{m}$ without modulo $π^{2}$ reduction for indices in which $1$ and $3$ appear alternately. We investigate those values th…

The International Linear Collider: Report to Snowmass 2021

Alexander Aryshev, Ties Behnke, Mikael Berggren +508

The International Linear Collider (ILC) is on the table now as a new global energy-frontier accelerator laboratory taking data in the 2030s. The ILC addresses key questions for our…

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.CO2021

Bijective enumerations for symmetrized poly-Bernoulli polynomials

Minoru Hirose, Toshiki Matsusaka, Ryutaro Sekigawa +1

Recently, Bényi and the second author introduced two combinatorial interpretations for symmetrized poly-Bernoulli polynomials. In the present study, we construct bijections between…

math.NT2021

Ohno relation for regularized multiple zeta values

Minoru Hirose, Hideki Murahara, Shingo Saito

The Ohno relation for multiple zeta values can be formulated as saying that a certain operator, defined for indices, is invariant under taking duals. In this paper, we generalize t…

math.NT2021

Ohno-type relation for interpolated multiple zeta values

Minoru Hirose, Hideki Murahara, Masataka Ono

We prove the Ohno-type relation for the interpolated multiple zeta values, which was introduced first by Yamamoto. Same type results for finite multiple zeta values are also given.…

Generating functions for sums of polynomial multiple zeta values

Minoru Hirose, Hideki Murahara, Shingo Saito

The sum formulas for multiple zeta(-star) values and symmetric multiple zeta(-star) values bear a striking resemblance. We explain the resemblance in a rather straightforward manne…

The motivic Galois group of mixed Tate motives over $Z [1/2]$ and its action on the fundamental group of $P^{1} ∖ {0, \pm 1, \infty}$

Minoru Hirose, Nobuo Sato

In this paper we introduce confluence relations for motivic Euler sums (also called alternating multiple zeta values) and show that all linear relations among motivic Euler sums ar…

The connector for Double Ohno relation

Minoru Hirose, Nobuo Sato, Shin-ichiro Seki

In this paper, we introduce a new connector which generalizes the connector found by the third author and Yamamoto. The new connector gives a direct proof of the double Ohno relati…

Modular phenomena for regularized double zeta values

Minoru Hirose

In this paper, we investigate linear relations among regularized motivic iterated integrals on $P^{1} ∖ {0, 1, \infty}$ of depth two, which we call regularized motiv…

math.NT2020★ 6 cited

On variants of symmetric multiple zeta-star values and the cyclic sum formula

Minoru Hirose, Hideki Murahara, Masataka Ono

The $t$ -adic symmetric multiple zeta values were defined Jarossay, which have been studied as a real analogue of $p$ -adic finite multiple zeta values. In this paper, w…

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.NT2019

Generating functions for Ohno type sums of finite and symmetric multiple zeta-star values

Minoru Hirose, Hideki Murahara, Shingo Saito

Ohno's relation states that a certain sum, which we call an Ohno type sum, of multiple zeta values remains unchanged if we replace the base index by its dual index. In view of Oyam…

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.

Double shuffle relations for refined symmetric multiple zeta values

Minoru Hirose

Symmetric multiple zeta values (SMZVs) are elements in the ring of all multiple zeta values modulo the ideal generated by $ζ (2)$ introduced by Kaneko-Zagier as counterparts of fini…

Weighted sum formula for multiple harmonic sums modulo primes

Minoru Hirose, Hideki Murahara, Shingo Saito

In this paper we prove a weighted sum formula for multiple harmonic sums modulo primes, thereby proving a weighted sum formula for finite multiple zeta values. Our proof utilizes d…