一类第二型Fuchs群的约化形式及其基本域

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(q~(1/2))为由形如(acq~(1/2)bq~(1/2)d)∈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(q~(1/2))作用在P2上的一个基本域的关系。

Reduce Form and Fundamental Domain of a Class of Second-Type Fuchs Groups

A class of second-type Fuchs group is defined,which is an important generalization of classical modular form. q is acted as a nature number which has no square factor. In the case ofq > 4 ,G(q~(1/2)) is defined as the group consisting of matrices in the form of (acq~(1/2)bq~(1/2)d) ∈SL(2,R) .Then the reduce form of all real positive quadratic formP2 under the action of G(q~(1/2)) is discussed. Finally,the relationship between the set of all reduce forms and the fundamental domain under the action of G(q~(1/2)) onP2 is given.