Congruence subgroups of Hecke groups

Hecke groups are an important tool in investigating functional equations, and congruence subgroups of Hecke groups play an important rule 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. Supported by NSF of China (No. 10571180) and the Guangdong Provincial Natural Science Foundation (No. 04009801)