Duke Mathematical Journal

Arithmetic groups and the length spectrum of Riemann surfaces

Paul Schmutz
Source: Duke Math. J. Volume 84, Number 1 (1996), 199-215.
First Page: Show Hide
Primary Subjects: 11F72
Secondary Subjects: 30F99, 58F17, 58G25
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077243633
Mathematical Reviews number (MathSciNet): MR1394753
Zentralblatt MATH identifier: 0867.30030
Digital Object Identifier: doi:10.1215/S0012-7094-96-08407-0

References

[1] A. Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485–535.
Mathematical Reviews (MathSciNet): MR26:5081
Zentralblatt MATH: 0107.14804
Digital Object Identifier: doi:10.2307/1970210
[2] P. Buser, Geometry and spectra of compact Riemann surfaces, Progress in Mathematics, vol. 106, Birkhäuser Boston Inc., Boston, MA, 1992.
Mathematical Reviews (MathSciNet): MR93g:58149
Zentralblatt MATH: 0770.53001
[3]1 H. Huber, Zur analytischen Theorie hyperbolischen Raumformen und Bewegungsgruppen, Math. Ann. 138 (1959), 1–26.
Mathematical Reviews (MathSciNet): MR22:99
Zentralblatt MATH: 0089.06101
Digital Object Identifier: doi:10.1007/BF01369663
[3]2 H. Huber, Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II, Math. Ann. 142 (1960/1961), 385–398.
Mathematical Reviews (MathSciNet): MR23:A3845
Zentralblatt MATH: 0094.05703
Digital Object Identifier: doi:10.1007/BF01451031
[4] S. Katok, Fuchsian groups, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1992.
Mathematical Reviews (MathSciNet): MR93d:20088
Zentralblatt MATH: 0753.30001
[5] W. Luo and P. Sarnak, Number variance for arithmetic hyperbolic surfaces, Comm. Math. Phys. 161 (1994), no. 2, 419–432.
Mathematical Reviews (MathSciNet): MR95k:11076
Zentralblatt MATH: 0797.58069
Digital Object Identifier: doi:10.1007/BF02099785
Project Euclid: euclid.cmp/1104269909
[6] W. Magnus, Noneuclidean tesselations and their groups, Pure and Applied Mathematics, vol. 61, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974.
Mathematical Reviews (MathSciNet): MR50:4774
Zentralblatt MATH: 0293.50002
[7] W. Müller, Spectral geometry and scattering theory for certain complete surfaces of finite volume, Invent. Math. 109 (1992), no. 2, 265–305.
Mathematical Reviews (MathSciNet): MR93g:58151
Zentralblatt MATH: 0772.58063
Digital Object Identifier: doi:10.1007/BF01232028
[8] A. M. Rockett and P. Szüsz, Continued fractions, World Scientific Publishing Co. Inc., River Edge, NJ, 1992.
Mathematical Reviews (MathSciNet): MR93m:11060
Zentralblatt MATH: 0925.11038
[9] P. Schmutz, Congruence subgroups and maximal Riemann surfaces, J. Geom. Anal. 4 (1994), no. 2, 207–218.
Mathematical Reviews (MathSciNet): MR95j:30039
Zentralblatt MATH: 0804.32010
[10] P. Schmutz, Riemann surfaces with shortest geodesic of maximal length, Geom. Funct. Anal. 3 (1993), no. 6, 564–631.
Mathematical Reviews (MathSciNet): MR95f:30060
Zentralblatt MATH: 0810.53034
Digital Object Identifier: doi:10.1007/BF01896258
[11] K. Takeuchi, Arithmetic triangle groups, J. Math. Soc. Japan 29 (1977), no. 1, 91–106.
Mathematical Reviews (MathSciNet): MR55:2754
Digital Object Identifier: doi:10.2969/jmsj/02910091
Project Euclid: euclid.jmsj/1240433796
[12] K. Takeuchi, A characterization of arithmetic Fuchsian groups, J. Math. Soc. Japan 27 (1975), no. 4, 600–612.
Mathematical Reviews (MathSciNet): MR53:2842
Zentralblatt MATH: 0311.20030
Digital Object Identifier: doi:10.2969/jmsj/02740600
Project Euclid: euclid.jmsj/1240434410
[13] M. F. Vignéras, Arithmétique des algèbres de quaternions, Lecture Notes in Math., vol. 800, Springer-Verlag, Berlin, 1980.
Mathematical Reviews (MathSciNet): MR82i:12016
Zentralblatt MATH: 0422.12008
[14] D. B. Zagier, Zetafunktionen und quadratische Körper, Springer-Verlag, Berlin, 1981.
Mathematical Reviews (MathSciNet): MR82m:10002
Zentralblatt MATH: 0459.10001

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?