一类第二型Fuchs群的约化形式及其基本域
, PP. 167-170
Keywords: 典型群,离散子群,约化形式,基本域,classicalgroup,discretegroup,reduceform,fundamentaldomain
Abstract:
:?定义一类二型Fuchs群,这类Fuchs群是经典模群PSL(2,Z)的重要推广。令q为不含平方因子的自然数,q>4,定义G(槡q)为由形如ab槡q槡()cqd∈SL(2,R)的矩阵构成的群。接着,讨论它作用在所有实正定二次型P2的约化形式。最后,给出所有这些约化形式构成的集合与G(槡q)作用在P2上的一个基本域的关系。
References
[1] | Schmidt T A. Sheingona M. On the infinite volume Hecke groups[J]. Compositio Math,1995,95(2): 247-262.
|
[2] | Chen B,Yuan P. Congruence subgroups of Hecke groups [J]. ActaMathematica Sinica,2009,25(6):931-944.
|
[3] | Miyake T. Modular Form [M]. Berlin Heidelberg,Springer-Verlag,2006: 43-63.
|
[4] | Wely H. Theory of reduction for arithmetical equivalence[J]. TranA. M. S,1940,48(1): 126-164.
|
[5] | Minkowski H. Gesammelte Abhandlungen[M]. Chelsea,New York,1967.
|
[6] | Rosen D,Schmidt T A. Hecke groups and continued fractions[J].Bull. Austral. Math. Soc,1992,46(3): 459-475.
|
[7] | Grenier D. Fundamental domains for the general linear group[J].Pac J Math,1988,132( 2): 247-262.
|
[8] | Rosen D. A Class of Continued Fractions Associated with CertainProperly Discontinuous Group[R]. Duke Math. J,1954,21(3):549-564.
|
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