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)

 

 

Classification of torsion-free genus zero congruence groups


Author: Abdellah Sebbar
Journal: Proc. Amer. Math. Soc. 129 (2001), 2517-2527
MSC (2000): Primary 20H05
DOI: https://doi.org/10.1090/S0002-9939-01-06176-7
Published electronically: April 17, 2001
MathSciNet review: 1838372
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

We study and classify all torsion-free genus zero congruence subgroups of the modular group.


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

  • 1. H. Larcher, The cusp amplitudes of the congruence subgroups of the classical modular group. II, Illinois J. Math. 28 (1984), no. 2, 312–338. MR 740621
  • 2. John McKay and Abdellah Sebbar, Fuchsian groups, Schwarzians, and theta functions, C. R. Acad. Sci. Paris Sér. I Math. 327 (1998), no. 4, 343–348 (English, with English and French summaries). MR 1650026, https://doi.org/10.1016/S0764-4442(99)80045-7
  • 3. McKay, J., Sebbar, Fuchsian groups, automorphic functions and Schwarzians, Math. Ann. 318 (2000), 255-275. CMP 2001:04
  • 4. Robert A. Rankin, Modular forms and functions, Cambridge University Press, Cambridge-New York-Melbourne, 1977. MR 0498390
  • 5. Sebbar A. Conjugacy classes of torsion-free genus zero congruence subgroups of ${\mbox{PSL}_2({\mathbb R})}$, To appear in Duke Math. J.
  • 6. Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Kanô Memorial Lectures, No. 1. MR 0314766

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20H05

Retrieve articles in all journals with MSC (2000): 20H05


Additional Information

Abdellah Sebbar
Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
Email: sebbar@mathstat.uottawa.ca

DOI: https://doi.org/10.1090/S0002-9939-01-06176-7
Keywords: Automorphic forms, congruence subgroups, genus 0, torsion-free
Received by editor(s): November 20, 1999
Published electronically: April 17, 2001
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 2001 American Mathematical Society