Normalizers of the congruence subgroups

of the Hecke group

Authors:
Mong-Lung Lang and Ser-Peow Tan

Journal:
Proc. Amer. Math. Soc. **127** (1999), 3131-3140

MSC (1991):
Primary 11F06

DOI:
https://doi.org/10.1090/S0002-9939-99-05154-0

Published electronically:
May 4, 1999

MathSciNet review:
1641120

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let cos and let be the Hecke group associated to . In this article, we show that for a prime ideal in , the congruence subgroups of are self-normalized in .

**[AL]**A. O. L. Atkin, J. Lehner,*Hecke operators on*, Math. Ann. , (), . MR**42:3022****[C]**J. H. Conway,*Understanding Groups like*, Groups, difference sets and the monster (Columbus, Ohio, 1993), Ohio State Univ. Math. Res. Inst. Publ., 4, de Gruyter, Berlin, 1996, 327-343. MR**98b:11041****[CLLT]**S. P. Chan, M. L. Lang, C. H. Lim, S. P. Tan,*The invariants of the congruence subgroups of the Hecke group*, Illinois J. of Math. (), .**[L1]**A. Leutbecher,*Uber die Heckeschen Gruppen*, Abh. Math. Sem. Hambg. (1967), . MR**37:4018****[L2]**A. Leutbecher,*Uber die Heckeschen Gruppen ,*, Math. Ann. (), . MR**50:238****[LT]**M. L. Lang, S. P. Tan,*Normalizer of the congruence subgroups of the Hecke groups and .*, (in preparation).**[LLT1]**M. L. Lang, C. H. Lim, S. P. Tan,*Independent generators for congruence subgroups of Hecke groups*, Math. Z. (1995), . MR**96k:11049****[LLT2]**M. L. Lang, C. H. Lim, S. P. Tan,*Principal congruence subgroups of the Hecke groups*, (submitted for publication).**[LN]**J. Lehner, M. Newman,*Weierstrass Point of*, Annals of Math. (1964), . MR**28:5045****[P]**L.A. Parson,*generalized Kloosterman sums and the Fourier coefficients of cusp forms*, Trans. Amer. Math. Soc. (), . MR**54:241****[R]**D. Rosen,*The substitutions of the Hecke group cos*, Arch. Math., (), . MR**87k:11048**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
11F06

Retrieve articles in all journals with MSC (1991): 11F06

Additional Information

**Mong-Lung Lang**

Affiliation:
Department of Mathematics, National University of Singapore, Singapore 119260, Republic of Singapore

Email:
matlml@math.nus.edu.sg

**Ser-Peow Tan**

Affiliation:
Department of Mathematics, National University of Singapore, Singapore 119260, Republic of Singapore

DOI:
https://doi.org/10.1090/S0002-9939-99-05154-0

Keywords:
Congruence subgroups,
Hecke groups

Received by editor(s):
January 10, 1998

Published electronically:
May 4, 1999

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1999
American Mathematical Society