Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Mong-Lung Lang; Ser-Peow Tan
Journal: Proc. Amer. Math. Soc. 128 (2000), 2271-2280.
MSC (1991): Primary 11F06
Posted: February 25, 2000
MathSciNet review: 1712893
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Let $\lambda = 2\cos(\pi /5)$ . Let $(\tau )$ be an ideal of $\mathbb{Z}[\lambda ]$ and let $(\tau _0)$ be the maximal ideal of $\mathbb{Z}[\lambda]$ such that $(\tau _0^2)\subseteq(\tau)$ . Then $N(G_0(\tau))\le G_0(\tau _0)$ . In particular, if $\tau$ is square free, then $G_{0}(\tau )$ is self-normalized in $PSL_{2}(\mathbb{R})$ .

References:

[AL]: A. O. L. Atkin, J. Lehner, Hecke operators on $\Gamma _{0}(m)$ , Math. Ann. 185, (1970), 134-160. MR 42:3022
[C]: J. H. Conway, Understanding Groups like $\Gamma _{0}(N)$ , 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. MR 95d:11047
[K]: R. S. Kulkarni, An Arithmetic-Geometric method in the study of subgroups of the Modular Groups. Amer. Jour. Math. 113 (1991), 1053-1134. MR 92i:11046
[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 $G(\lambda )$ , , Math. Ann. 211 (1974), 63-68. MR 50:238
[LT1]: M. L. Lang, S. P. Tan, Normalizer of the congruence subgroups of the Hecke groups $G_{4}$ and $G_{6}$ , preprint.
[LT2]: M. L. Lang, S. P. Tan, Normalizer of the congruence subgroups of the Hecke group $G_{5}$ , Proc. Amer. Math. Soc. 127 (1999), 3131-3140. CMP 99:17
[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 Points of $\Gamma _{0}(N)$ , 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, A class of continued fractions associated with certain properly discontinuous groups, Duke Math., 21(1954), 549-563. MR 16:458d

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|