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It is well-known that if a convex hyperbolic
polygon is constructed as a fundamental domain for a subgroup of
the modular group, then its translates by the group elements form
a locally finite tessellation and its side-pairing transformations
form a system of generators for the group. Such hyperbolically
convex polygons can be obtained by using Dirichlet's and Ford's
polygon constructions. Another method of obtaining a fundamental
domain for subgroups of the modular group is through the use of a
right coset decomposition and we call such domains standard
fundamental domains. In this paper we give subgroups of the
modular group which do not have hyperbolically convex standard
fundamental domain containing only inequivalent cusps.
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참고문헌 (9)
참고문헌 신청
A. F. Beardon / 1983 / The Geometry of Discrete Groups, Graduate Texts in Mathematics / Springer-Verlag : 91 ~
D. Zagier / 1985 / parametrizations of elliptic curves / Canad. Math. Bull 28 (3) : 372 ~ 384
H. Iwaniec / 1997 / Topics in Classical Automorphic Forms, Graduate Studies in Mathematics / American Mathematical Society, Providence, RI : 17 ~
H. Tietze / 1928 / Uber Konvexheit im kleinen und im gro?en und ¨uber gewisse den Punkten einer Menge zugeordnete Dimensionszahlen / Math. Z. 28 (1) : 697 ~ 707
J. Lehner / 1964 / Discontinuous Groups and Automorphic Functions / American Mathematical Society, Providence, R.I
D. Zagier / 1985 / parametrizations of elliptic curves / Canad. Math. Bull 28 (3) : 372 ~ 384
H. Iwaniec / 1997 / Topics in Classical Automorphic Forms, Graduate Studies in Mathematics / American Mathematical Society, Providence, RI : 17 ~
H. Tietze / 1928 / Uber Konvexheit im kleinen und im gro?en und ¨uber gewisse den Punkten einer Menge zugeordnete Dimensionszahlen / Math. Z. 28 (1) : 697 ~ 707
J. Lehner / 1964 / Discontinuous Groups and Automorphic Functions / American Mathematical Society, Providence, R.I
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