Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-24T16:38:28.465Z Has data issue: false hasContentIssue false
  • English
  • Français

On Hurwitz Constants for Fuchsian Groups

Published online by Cambridge University Press:  20 November 2018

L. Ya. Vulakh
L. Ya. Vulakh*
Affiliation:
Department of Mathematics, The Cooper Union, 51 Astor Place, New York, New York 10003, U.S.A. e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Explicit bounds for the Hurwitz constants for general cofinite Fuchsian groups have been found. It is shown that the bounds obtained are exact for the Hecke groups and triangular groups with signature (0 : 2, p, q).

Keywords

11J0420H10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 2 , 01 April 1997 , pp. 406 - 417
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Beardon, A.F., The Geometry of Discrete Groups, Springer-Verlag, New York, 1983.Google Scholar
2. Cassels, J.W.S., An introduction to Diophantine approximation, Cambridge Univ. Press, 1957.Google Scholar
3. Ford, L.R., A geometric proof of a theorem of Hurwitz, Proc. Edinburgh Math. Soc. 35(1917), 59–65.Google Scholar
4. Haas, A. and Series, C., TheHurwitz constant and Diophantine approximation on Hecke groups, J. London Math. Soc. (2) 34(1986), 219–234.Google Scholar
5. Hurwitz, A., Über die angenaherte Darstellungen der Irrationalzahlen durch rationale Brüche’, Math. Ann. 39(1891), 279–284.Google Scholar
6. Lehner, J., Diophantine approximation of Fuchsian groups, Pacific J. Math. 2(1952), 327–333.Google Scholar
7. Lehner, J., Diophantine approximation on Hecke groups, Glasgow Math. J. 27(1985), 117–127.Google Scholar
8. Lehner, J., The local Hurwitz constant and Diophantine approximation on Hecke groups, Math. Comp. (55) 192(1990), 765–781.Google Scholar
9. Magnus, W., Noneuclidean Tessellations and Their Groups, Academic Press, New York and London, 1974.Google Scholar
10. Rankin, R.A., Diophantine approximation and horocyclic groups, Canad. J. Math. 9(1957), 155–182.Google Scholar
11. Vulakh, L.Ya., Diophantine approximation on Bianchi groups, J. Number Theory 54(1995), 73–80.Google Scholar
12. Vulakh, L.Ya., Diophantine approximation in Rn, Trans. Amer.Math. Soc. 347(1995), 573–585.Google Scholar