Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Normalizers of the congruence subgroups
of the Hecke group $G_{5}$


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 $\lambda = 2$cos$(\pi /5)$ and let $G$ be the Hecke group associated to $\lambda $. In this article, we show that for $\tau $ a prime ideal in $\mathbb{Z}[\lambda ]$, the congruence subgroups $G_{0}(\tau )$ of $G$ are self-normalized in $PSL_{2}(\mathbb{R})$.


References [Enhancements On Off] (What's this?)

  • [AL] A. O. L. Atkin, J. Lehner, Hecke operators on $\Gamma _{o}(m)$, Math. Ann. $185$, ($1970$), $134-160$. MR 42:3022
  • [C] J. H. Conway, Understanding Groups like $\Gamma _{o}(N)$, 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 $G_{0}(P)$ of the Hecke group, Illinois J. of Math. $38$ ($1994$), $636-652$.
  • [L1] A. Leutbecher, Uber die Heckeschen Gruppen $G(\lambda )$, Abh. Math. Sem. Hambg. $31$ (1967), $199-205$. MR 37:4018
  • [L2] A. Leutbecher, Uber die Heckeschen Gruppen $G(\lambda )$, $II$, Math. Ann. $211$ ($1974$), $63-68$. MR 50:238
  • [LT] M. L. Lang, S. P. Tan, Normalizer of the congruence subgroups of the Hecke groups $G_{4}$ and $G_{6}$., (in preparation).
  • [LLT1] M. L. Lang, C. H. Lim, S. P. Tan, Independent generators for congruence subgroups of Hecke groups, Math. Z. $220$ (1995), $569-594$. 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 $\Gamma _{o}(N)$, Annals of Math. $79$ (1964), $360-368$. MR 28:5045
  • [P] L.A. Parson, generalized Kloosterman sums and the Fourier coefficients of cusp forms, Trans. Amer. Math. Soc. $217$ ($1976$), $329-350$. MR 54:241
  • [R] D. Rosen, The substitutions of the Hecke group $\Gamma (2$cos$\pi /5)$, Arch. Math., $46$ ($1986$), $533-538$. MR 87k:11048

Similar Articles

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

American Mathematical Society