研究者詳細 - 古庄　英和

論文 - 古庄　英和

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Notes on Kashiwara-Vergne and double shuffle Lie algebras 招待有り査読有り

Hidekazu Furusho and Nao Komiyama

Low Dimensional Topology and Number Theory Fukuoka, Japan, March 15–18, 2022. In Memory of Professor Toshie Takata 2025年3月

The stabilizer bitorsors of the module and algebra harmonic coproducts are equal

Enriquez, B; Furusho, H

ADVANCES IN MATHEMATICS 463 巻 2025年3月

The Betti side of the double shuffle theory. III. Bitorsor structures 査読有り

Enriquez, B; Furusho, H

SELECTA MATHEMATICA-NEW SERIES 29 巻 ( 2 ) 2023年4月

The Betti side of the double shuffle theory. II. Double shuffle relations for associators 査読有り

Enriquez, B; Furusho, H

SELECTA MATHEMATICA-NEW SERIES 29 巻 ( 1 ) 2023年2月

The l-adic hypergeometric function and associators

Furusho, H

TUNISIAN JOURNAL OF MATHEMATICS 5 巻 ( 1 ) 頁： 1 - 29 2023年

Kashiwara-Vergne and dihedral bigraded Lie algebras in mould theory 査読有り

Hidekazu Furusho and Nao Komiyama

Ann. Fac. Sci. Toulouse Math XXXII 巻 ( 4 ) 頁： 655 - 725 2023年

THE PENTAGON EQUATION AND THE CONFLUENCE RELATIONS 査読有り

Furusho, H

AMERICAN JOURNAL OF MATHEMATICS 144 巻 ( 4 ) 頁： 873 - 894 2022年8月

On relations among multiple zeta values obtained in knot theory 招待有り査読有り

Hidekazu Furusho

the Advanced Lectures in Mathematics (ALM) book series 49 巻頁： 73 - 89 2022年

Analytic continuation of multiple polylogarithms in positive characteristic 査読有り

Furusho, H

TUNISIAN JOURNAL OF MATHEMATICS 4 巻 ( 3 ) 2022年

The Betti side of the double shuffle theory. I. The harmonic coproducts 査読有り

Enriquez, B; Furusho, H

SELECTA MATHEMATICA-NEW SERIES 27 巻 ( 5 ) 2021年11月

Galois action on knots II: proalgebraic string links and knots 招待有り査読有り

Hidekazu Furusho

Periods in Quantum Field Theory and Arithmetic" Springer Proceedings in Mathematics & Statistics 314 巻頁： 541--591 2020年3月

p-adic multiple L-functions and cyclotomic multiple harmonic values 査読有り

Furusho Hidekazu, Jarossay David

INTERNATIONAL JOURNAL OF NUMBER THEORY 16 巻 ( 2 ) 頁： 361 - 375 2020年3月

A Stabilizer Interpretation of Double Shuffle Lie Algebras 査読有り

Enriquez, B; Furusho, H

INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2018 巻 ( 22 ) 頁： 6870 - 6907 2018年11月

On the coefficients of the Alekseev-Torossian associator 査読有り

Furusho, H

JOURNAL OF ALGEBRA 506 巻頁： 364 - 378 2018年7月

DESINGULARIZATION OF COMPLEX MULTIPLE ZETA-FUNCTIONS 査読有り

Furusho, H; Komori, Y; Matsumoto, K; Tsumura, H

AMERICAN JOURNAL OF MATHEMATICS 139 巻 ( 1 ) 頁： 147 - 173 2017年2月

Fundamentals of <i>p</i>-adic multiple <i>L</i>-functions and evaluation of their special values 査読有り

Furusho, H; Komori, Y; Matsumoto, K; Tsumura, H

SELECTA MATHEMATICA-NEW SERIES 23 巻 ( 1 ) 頁： 39 - 100 2017年1月

Galois action on knots I: Action of the absolute Galois group 査読有り

Furusho, H

QUANTUM TOPOLOGY 8 巻 ( 2 ) 頁： 295 - 360 2017年

p-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas, 査読有り

Hidekazu Furusho, Shinichi Kobayashi, Kenichi Bannai

Nagoya Math Journal 219 巻頁： 269-302 2015年

Around associators 招待有り査読有り

Hidekazu Furusho

Automorphic forms and Galois representations 2 ( 415 ) 頁： 105-117 2014年

Mixed Pentagon, octagon and Broadhurst duality equation 査読有り

Benjamin Enriquez, Hidekazu Furusho

Journal of Pure and Applied Algebra 216 巻 ( 4 ) 頁： 982-995 2012年

Geometric interpretation of double shuffle relation for multiple L-values 査読有り

Hidekazu Furusho

Galois-Teichm\"{u}ller theory and Arithmetic Geometry, Advanced Studies in Pure Math 63 巻頁： 163-187 2012年

Double shuffle relation for associators 査読有り

Hidekazu Furusho

Annals of Mathematics 174 巻 ( 1 ) 頁： 341-360 2011年

Pentagon and hexagon equations 査読有り

Hidekazu Furusho

Annals of Mathematics 171 巻 ( 1 ) 頁： 545-556 2010年

Algebraic cycles and motivic generic iterated integrals 査読有り

Hidekazu Furusho, Amir Jafari

Mathematical Research Letters 14 巻 ( 6 ) 頁： 923-942 2007年

Regularization and generalized double shuffle relations for p-adic multiple zeta values 査読有り

Hidekazu Furusho, Amir Jafari

Compositio Math 143 巻頁： 1089-1107 2007年

p-adic multiple zeta values II -- tannakian interpretations 査読有り

Hidekazu Furusho

Amer.J.Math 129 巻 ( 4 ) 頁： 1105-1144 2007年

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

We establish a tannakian formalism of $p$-adic multiple polylogarithms
and $p$-adic multiple zeta values introduced in our previous paper
via a comparison isomorphism between
a de Rham fundamental torsor and a rigid fundamental torsor
of the projective line minus three points
and also discuss its Hodge and \'{e}tale analogues.
As an application we give a way to erase log poles of
$p$-adic multiple polylogarithms and introduce
overconvergent $p$-adic multiple polylogarithms
which might be $p$-adic multiple analogue of
Zagier's single-valued complex polylogarithms.

p-adic multiple zeta values -- a precis. p-adic mathmatical physics 招待有り査読有り

Hidekazu Furusho

Amer.Inst.Phys 826 巻頁： 222-236 2006年

記述言語：英語掲載種別：研究論文（学術雑誌）

This is an expose of the theory of $p$-adic multiple zeta value
developped by the author.
This theory is almost parallel to the story of the complex case.
$p$-adic multiple polylogarithm, which is a $p$-adic function,
is constructed by Coleman's $p$-adic iterated integration theory.
$p$-adic multiple zeta value is defined to be its special value at $1$.
Many nice properties of $p$-adic multiple zeta value is shown.
$p$-adic KZ equation is also introduced and the $p$-adic Drinfel'd associator
is constructed from two fundamental solutions of the $p$-adic KZ equation.
A relation of $p$-adic multiple zeta value with
the $p$-adic Drinfel'd associator as well as
its relation with the fundamental group of the projective line minus
three points is established.

Multiple zeta values and Grothendieck-Teichm\"{u}ller groups 招待有り査読有り

Hidekazu Furusho

AMS Contemporary Math 416 巻頁： 49-82 2006年

記述言語：英語掲載種別：研究論文（学術雑誌）

We get a canonical embedding from the spectrum of the algebra
of multiple zeta values modulo $\pi^2$ into the graded version of
the Grothendieck-Teichm\"{u}ller group
by using relations of the Drinfel'd associator.
On the other hand, it is known that the
rational pro-$l$ Galois image algebraic group
is embedded into the Grothendieck-Teichm\"{u}ller
pro-algebraic group for each prime $l$.
Via these embeddings, we get two kinds of relationship
between the spectrum of the algebra of multiple zeta values and
the pro-$l$ Galois image algebraic group.

The double shuffle relations for p-adic multiple zeta values 招待有り査読有り

Hidekazu Furusho, Amnon Besser

AMS Contemporary Math 416 巻頁： 9-29 2006年

p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation 査読有り

Hidekazu Furusho

Inventiones Mathematicae 155 巻 ( 2 ) 頁： 253-286 2004年

記述言語：英語掲載種別：研究論文（学術雑誌）

Our main aim in this paper is to give a foundation of the theory of
$p$-adic multiple zeta values.
We introduce (one variable) $p$-adic multiple polylogarithms
by Coleman's $p$-adic iterated integration theory.
We define $p$-adic multiple zeta values to be special values of
$p$-adic multiple polylogarithms.
We consider the $p$-adic KZ equation and introduce the
$p$-adic Drinfel'd associator
by using certain two fundamental solutions of the $p$-adic KZ equation.
We show that our $p$-adic multiple polylogarithms appear
as coefficients of
a certain fundamental solution of the $p$-adic KZ equation
and our $p$-adic multiple zeta values appear
as coefficients of the $p$-adic Drinfel'd associator.
We show various properties of $p$-adic multiple zeta values,
which are sometimes analogous to the complex case
and are sometimes peculiar to the $p$-adic case,
via the $p$-adic KZ equation.

The multiple zeta value algebra and the stable derivation algebra 査読有り

Hidekazu Furusho

Publ. Res. Inst. Math. Sci. 39 巻 ( 4 ) 頁： 695-720 2003年

Geometric and arithmetic subgroups of the Grothendieck-Teichm\"{u}ller group 査読有り

Hidekazu Furusho

Mathematical Research Letters 10 巻 ( 1 ) 頁： 97-108 2003年

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