論文 - 古庄　英和

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

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

Double shuffle relation for associators 査読有り

Hidekazu Furusho

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

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

Pentagon and hexagon equations 査読有り

Hidekazu Furusho

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

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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）  

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

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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.

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

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

We give a proof of double shuffle relations for $p$-adic multiple zeta values
by developing higher dimensional version of tangential base points and
discussing a relationship with two (and one) variable $p$-adic multiple
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

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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

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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.

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

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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

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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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記述言語：英語   掲載種別：研究論文（学術雑誌）