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Congruence Subgroups of Hecke Groups 被引量：1

Congruence Subgroups of Hecke Groups
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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.
作者 Bo CHEN Ping Zhi YUAN
机构地区 School of Science School of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 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)
关键词 Hecke group principal congruence subgroup congruence subgroup Hecke group, principal congruence subgroup, congruence subgroup
分类号 O152.7 [理学—基础数学] O156.4 [理学—基础数学]
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参考文献15

  • 1Hecke, E: Uber die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung. Math. Ann., 112, 664-699 .(1936).
  • 2Cangiil, i-N., Singerman, D.: Normal subgroups of Hecke groups and regular maps. Math. Proc. Camb. Phil. Soc., 123(1), 59-74 (1998).
  • 3Schmidt, T.-A., Sheingorn, M.: Length spectra of the Hecke triangle groups. Math. Z., 220(3), 369-397 (1995).
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同被引文献7

  • 1Miyake T. Modular Form [ M ]. Berlin Heidelberg, Springer-Verlag, 2006:43 -63.
  • 2Wely H. Theory of reduction for arithmetical equivalence [ J ]. Tran A.M.S, 1940, 48(1): 126-164.
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  • 6Rosen D. A Class of Continued Fractions Associated with Certain Properly Discontinuous Group [ R ]. Duke Math. J, 1954, 21 (3) : 549 - 564.
  • 7Schmidt T A. Sheingona M. On the infinite volume Hecke groups [J]. Compositio Math, 1995, 95(2) : 247 -262.

引证文献1

Acta Mathematica Sinica,English Series
2009年 第6期

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