start-ver=1.4
cd-journal=joma
no-vol=55
cd-vols=
no-issue=1
article-no=
start-page=191
end-page=200
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2013
dt-pub=201301
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=ON HYPERBOLIC AREA OF THE MODULI OF �Ɓ|ACUTE TRIANGLES
en-subtitle=
kn-subtitle=
en-abstract=
kn-abstract=A ��-acute triangle is a Euclidean triangle on the plane
whose three angles are less than a given constant ��. In this note, we
shall give an explicit formula computing the hyperbolic area A(��) of
the moduli region of ��-acute triangles on the Poincar�Le disk. It turns
out that A(��) is a period in the sense of Kontsevich-Zagier if cot �� is a
nonnegative algebraic number.
en-copyright=
kn-copyright=

en-aut-name=KanesakaNaomi
en-aut-sei=Kanesaka
en-aut-mei=Naomi
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

en-aut-name=NakamuraHiroaki
en-aut-sei=Nakamura
en-aut-mei=Hiroaki
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=2
ORCID=

affil-num=1
en-affil=
kn-affil=Department of Mathematics, Faculty of Science, Okayama University

affil-num=2
en-affil=
kn-affil=Department of Mathematics, Faculty of Science, Okayama University
en-keyword=moduli space
kn-keyword=moduli space
en-keyword=Euclidean triangle
kn-keyword=Euclidean triangle
en-keyword=hyperbolic measure
kn-keyword=hyperbolic measure
END

start-ver=1.4
cd-journal=joma
no-vol=12
cd-vols=
no-issue=
article-no=
start-page=123
end-page=133
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2006
dt-pub=20060824
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=Some classical views on the parameters of the Grothendieck-Teichm?eller group
en-subtitle=
kn-subtitle=
en-abstract=
kn-abstract=<p>We present two new formulas concerning behaviors of the standard parameters of the Grothendieck-Teichm?ller group GT , and discuss their relationships with classical mathematics. First, considering a non-Galois etale cover of P<sub>1</sub> {0 1 infinity} of degree 4, we present a newtype equation satisfied by the Galois image in GT . Second, a certain equation in GL <sub>2</sub> (Z||Z<sub>2</sub> ) satisfied by every element of GT is derived as an application of (profinite) free differential calculus.</p>

en-copyright=
kn-copyright=

en-aut-name=NakamuraHiroaki
en-aut-sei=Nakamura
en-aut-mei=Hiroaki
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

affil-num=1
en-affil=
kn-affil=Okayama University
en-keyword=Grothendieck-Teichm?eller group
kn-keyword=Grothendieck-Teichm?eller group
en-keyword=Belyi function
kn-keyword=Belyi function
en-keyword=modular function
kn-keyword=modular function
END

start-ver=1.4
cd-journal=joma
no-vol=46
cd-vols=
no-issue=1
article-no=
start-page=39
end-page=76
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2004
dt-pub=200401
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=Eigenloci of 5 Point Configurations on the Riemann Sphere and the Grothendieck-Teichm&#12539;ler Group
en-subtitle=
kn-subtitle=
en-abstract=
kn-abstract=
en-copyright=
kn-copyright=

en-aut-name=LochakPierre
en-aut-sei=Lochak
en-aut-mei=Pierre
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

en-aut-name=NakamuraHiroaki
en-aut-sei=Nakamura
en-aut-mei=Hiroaki
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=2
ORCID=

en-aut-name=SchnepsLeila
en-aut-sei=Schneps
en-aut-mei=Leila
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=3
ORCID=

affil-num=1
en-affil=
kn-affil=175 rue de Chevaleret

affil-num=2
en-affil=
kn-affil=Okayama University

affil-num=3
en-affil=
kn-affil=175 rue de Chevaleret
en-keyword=Riemann Spheres;Point Configurations;Grothendieck-Teichm?ler Group;Galois Group;Rational Numbers;Modular Group
kn-keyword=Riemann Spheres;Point Configurations;Grothendieck-Teichm?ler Group;Galois Group;Rational Numbers;Modular Group
END

start-ver=1.4
cd-journal=joma
no-vol=52
cd-vols=
no-issue=1
article-no=
start-page=61
end-page=63
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2010
dt-pub=201001
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=BELYI FUNCTION ON X<sub>0</sub>(49) OF DEGREE 7
en-subtitle=
kn-subtitle=
en-abstract=
kn-abstract=
en-copyright=
kn-copyright=

en-aut-name=HoshinoKenji
en-aut-sei=Hoshino
en-aut-mei=Kenji
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

en-aut-name=NakamuraHiroaki
en-aut-sei=Nakamura
en-aut-mei=Hiroaki
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=2
ORCID=

affil-num=1
en-affil=
kn-affil=Department of Mathematics, Faculty of Science, Okayama University

affil-num=2
en-affil=
kn-affil=Department of Mathematics, Faculty of Science, Okayama University
END