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

Remote Access
Gold Open Access
Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173


Some presentations for $\overline{\Gamma}_0(N)$

Author: Antonio Lascurain Orive
Journal: Conform. Geom. Dyn. 6 (2002), 33-60
MSC (2000): Primary 11F06, 20H05, 30F35, 51M10, 52C22; Secondary 13M05, 22E40
Published electronically: May 30, 2002
MathSciNet review: 1948848
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Some presentations of the Fuchsian groups defined by the Hecke congruence subgroups

\begin{displaymath}\Gamma_{0}( N)\;=\; \left\{\begin{pmatrix} a& b \\ c& d \en... ...} )\;\Big {\vert} \;\; c\equiv 0\;\; \text{mod}\; N \right\} \end{displaymath}

are given. The first is one obtained by the Reidemeister-Schreier rewriting process, thereby completing and correcting Chuman's work on the subject. The main result (Theorem 3) is the reduction of this huge presentation into another one which is simple and useful. In the process, $\mathbb{Z} _N$ is partitioned into three subsets that exhibit many cyclic and dual properties of its ring structure. For some cases, a minimal presentation derived from the Ford domains is given explicitly in terms of the units and its inverses.

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

Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2000): 11F06, 20H05, 30F35, 51M10, 52C22, 13M05, 22E40

Retrieve articles in all journals with MSC (2000): 11F06, 20H05, 30F35, 51M10, 52C22, 13M05, 22E40

Additional Information

Antonio Lascurain Orive
Affiliation: Havre 101, Colonia Villa Verdun, Mexico D.F. 01810 Mexico

PII: S 1088-4173(02)00073-5
Received by editor(s): January 8, 2001
Received by editor(s) in revised form: April 11, 2002
Published electronically: May 30, 2002
Article copyright: © Copyright 2002 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia