The Ramanujan Journal 38(3) 455-463 Dec 2015 [Refereed]

From the theory of modular forms, there are exactly linear
relations among the Eisenstein series and its products . We present explicit formulas among these modular forms
based on the partial f...

In this paper, we study specific families of multiple zeta values which
closely relate to the linear part of Kawashima's relation. We obtain an
explicit basis of these families, and investigate their interpolations to
complex functions. As a corol...

Ihara, Kaneko, and Zagier defined two regularizations of multiple zeta values
and proved the regularization theorem that describes the relation between those
regularizations. We show that the regularization theorem can be generalized to
polynomial...

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.

Symmetric multiple zeta values (SMZVs) are elements in the ring of all
multiple zeta values modulo the ideal generated by introduced by
Kaneko-Zagier as counterparts of finite multiple zeta values. It is known that
symmetric multiple ze...

We consider a cyclic analogue of multiple zeta values (CMZVs), which has two
kinds of expressions; series and integral expression. We prove an
`integralseries' type identity for CMZVs. By using this identity, we
construct two classes of $\mathb...

Symmetric multiple zeta values (SMZVs) are elements in the ring of all
multiple zeta values modulo the ideal generated by introduced by
Kaneko-Zagier as counterparts of finite multiple zeta values. It is known that
symmetric multiple ze...

Ohno's relation is a generalization of both the sum formula and the duality
formula for multiple zeta values. Oyama gave a similar relation for finite
multiple zeta values, defined by Kaneko and Zagier. In this paper, we prove
relations of similar...

In this paper we consider iterated integrals on
and define a class of
-linear relations among them, which arises from the differential
structure of the iterated integrals with respect to . W...

In this paper we prove certain algebraic identities, which correspond to
differentiations of the shuffle relation, the stuffle relation, and the
relations which arise from Möbius transformations of iterated integrals.
These formulas provide fund...

Minoru Hirose, Kohei Iwaki, Nobuo Sato, Koji Tasaka

Apr 2017

We investigate linear relations among a class of iterated integrals on the
Riemann sphere minus four points and . Generalization of the
duality formula and the sum formula for multiple zeta values to the iterated
integrals are given.

In this paper, we shall prove the equality \[
\zeta(3,\{2\}^{n},1,2)=\zeta(\{2\}^{n+3})+2\zeta(3,3,\{2\}^{n}) \] conjectured
by Hoffman using certain identities among iterated integrals on
.

In 1988, Gross proposed a conjectural congruence between Stickelberger
elements and algebraic regulators, which is often referred to as the refined
class number formula. In this paper, we prove this congruence.

We introduce the notion of Shintani data, which axiomatizes algebraic aspects
of Shintani zeta functions. We develop the general theory of Shintani data, and
show that the order of vanishing part of Gross's conjecture follows from the
existence of...

In this paper, we introduce the normalized Shintani L-function of several
variables by an integral representation and prove its functional equation. The
Shintani L-function is a generalization to several variables of the
Hurwitz-Lerch zeta functio...

We define the class of normalized Shintani L-functions of several variables.
Unlike Shintani zeta functions, the normalized Shintani L-function is a
holomorphic function. Moreover it satisfies a good functional equation. We show
that any Hecke L-f...

Multiple zeta values and modular forms for certain congruence subgroups

Minoru Hirose

The 12th Young Mathematicians Conference on Zeta Functions 17 Feb 2019

Multiple zeta values and iterated integrals

Minoru Hirose

20 Oct 2018

Iterated Integrals and Refinements of Symmetric Multiple Zeta Values

Minoru Hirose

Taiwan-Japan Joint Workshop on Multiple Zeta Values 2 Aug 2018

Generalization of Zagier's 2-3-2 formula of multiple zeta values

Minoru Hirose

Ehime University Algebra Seminar 20 Jul 2018

Block shuffle identity for multiple zeta values

Minoru Hirose

2018 Number Theory Workshop at Waseda University 14 Mar 2018

On a certain class of linear relations among the multiple zeta values

Minoru Hirose

The 11th Young Mathematicians Conference on Zeta Functions 21 Feb 2018

Iterated integrals and symmetrized multiple zeta values

Minoru Hirose

MZV Days at HIM 30 Jan 2018

Confluence relations of multiple zeta values

Minoru Hirose

HIM Workshop "Periods and Regulators" 19 Jan 2018

On the Charlton's conjecture and its generalization for multiple zeta values

Minoru Hirose

38th Kansai Multiple Zeta Seminar 9 Dec 2017

On a certain class of linear relations among the multiple zeta values arising from the theory of iterated integrals

Minoru Hirose

3rd Japanese-German Number Theory Workshop 22 Nov 2017

A generalized cyclic sum formula for iterated integrals

Minoru Hirose

Polylogs, multiple zetas, and related topics 11 Nov 2017

On the Charlton's conjecture and its generalization for multiple zeta values

Minoru Hirose

Kyushu University Algebra Seminar 20 Oct 2017

Enhanced regulators and p-adic L-functions

Minoru Hirose

Regulators in Niseko 2017 5 Sep 2017

On certain identities among the multiple zeta values

Minoru Hirose

11th Hukuoka Number Theory Workshop 10 Aug 2017

On Gross’s refined class number formula and enhanced Stickelberger elements

Minoru Hirose

16th Hiroshima-Sendai Number Theory Workshop 12 Jul 2017

On the Gross’s refined class number formula

Minoru Hirose

P-adic Arithmetic Geometry and Related Topics” Seminar 25 Apr 2017

A certain combinatorial module inspired by the Goncharov coproduct

Minoru Hirose

Various Aspects of Multiple Zeta Values 12 Jul 2016

Shintani zeta functions and Gross conjecture

Minoru Hirose

Algebraic Number Theory and Related Topics 30 Nov 2015

On an enhancement of the Stark conjecture, the Zagier conjecture and the Gross conjecture on the special values of complex and p-adic L-functions of number fields

Minoru Hirose

Arithmetic Geometry Seminar Nov 2015

On a refinement of Rubin-Stark conjecture

Minoru Hirose

Number Theory Seminar 19 Jun 2015

Conjectural construction of Rubin-Stark elements by Shintani method and generalization of Dasgupta’s conjecture to the higher rank case

Minoru Hirose

Osaka University Number theory and automorphic seminar 15 May 2015

The partial derivatives of abelian L-functions at s=0 and refinement of Stark conjecture

Minoru Hirose

Japan-Korea Joint Seminar on Number Theory and Related Topics 2014 19 Nov 2014

On the normalized Shintani L-functions and Hecke L-functions of totally real fields

Minoru Hirose

Kobe University Algebraic Seminar 23 Oct 2014

On the theory of fans and its application to Shintani L-function and Hecke L-function

Minoru Hirose

Number Theory Workshop at Waseda University 13 Mar 2014

On the normalized Shintani L-function and Hecke L-function of totally real ﬁelds

Minoru Hirose

RIMS conference "Automorphic Forms and Related Zeta Functions" 20 Jan 2014

On a construction of Hecke L-function by normalized Shintani L-functions

Minoru Hirose

Number Theory Seminar 25 Oct 2013

On the Shintani L-function 2

Minoru Hirose

27th Automorphic Forms Workshop 12 Mar 2013

On the Shintani L-function 2

Minoru Hirose

6th Multiple Zeta Values Workshop 23 Feb 2013

On the functional equation of the Shintani L-function

Nobuo Sato, Minoru Hirose

RIMS Conference Automorphic forms and automorphic L-functions 18 Jan 2012