Congruence Subgroups of Hecke Groups  

作　　者：Bo CHEN Ping Zhi YUAN 

机构地区：[1]School of Science, Chongqing Jiaotong University, Chongqing 400074, P. R. China [2]School of Mathematics, South China Normal University, Guangzhou 510631, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第6期931-944,共14页数学学报（英文版）

基　　金：NSF of China(No.10571180);the Guangdong Provincial Natural Science Foundation(No.04009801)

摘　　要：Hecke groups are an important tool in subgroups of Hecke groups play an important rule investigating functional equations, and congruence in research of the solutions of the Dirichlet series. When q, m are two primes, congruence subgroups and the principal congruence subgroups of level m of the Hecke group H（√q） have been investigated in many papers. In this paper, we generalize these results to the case where q is a positive integer with q ≥ 5, √q ￠ Z and m is a power of an odd prime.Hecke groups are an important tool in subgroups of Hecke groups play an important rule investigating functional equations, and congruence in research of the solutions of the Dirichlet series. When q, m are two primes, congruence subgroups and the principal congruence subgroups of level m of the Hecke group H（√q） have been investigated in many papers. In this paper, we generalize these results to the case where q is a positive integer with q ≥ 5, √q ￠ Z and m is a power of an odd prime.

关 键 词：Hecke group principal congruence subgroup congruence subgroup 

分 类 号：O152.7[理学—数学] O156.4[理学—基础数学]