Duke Mathematical Journal

Arithmetic groups and the length spectrum of Riemann surfaces

Paul Schmutz

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Article information

Duke Math. J. Volume 84, Number 1 (1996), 199-215.

First available: 19 February 2004

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Primary: 11F72: Spectral theory; Selberg trace formula
Secondary: 30F99: None of the above, but in this section 58F17 58G25


Schmutz, Paul. Arithmetic groups and the length spectrum of Riemann surfaces. Duke Mathematical Journal 84 (1996), no. 1, 199--215. doi:10.1215/S0012-7094-96-08407-0. http://projecteuclid.org/euclid.dmj/1077243633.

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  • [1] A. Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485–535.
  • [2] P. Buser, Geometry and spectra of compact Riemann surfaces, Progress in Mathematics, vol. 106, Birkhäuser Boston Inc., Boston, MA, 1992.
  • [3]1 H. Huber, Zur analytischen Theorie hyperbolischen Raumformen und Bewegungsgruppen, Math. Ann. 138 (1959), 1–26.
  • [3]2 H. Huber, Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II, Math. Ann. 142 (1960/1961), 385–398.
  • [4] S. Katok, Fuchsian groups, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1992.
  • [5] W. Luo and P. Sarnak, Number variance for arithmetic hyperbolic surfaces, Comm. Math. Phys. 161 (1994), no. 2, 419–432.
  • [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.
  • [7] W. Müller, Spectral geometry and scattering theory for certain complete surfaces of finite volume, Invent. Math. 109 (1992), no. 2, 265–305.
  • [8] A. M. Rockett and P. Szüsz, Continued fractions, World Scientific Publishing Co. Inc., River Edge, NJ, 1992.
  • [9] P. Schmutz, Congruence subgroups and maximal Riemann surfaces, J. Geom. Anal. 4 (1994), no. 2, 207–218.
  • [10] P. Schmutz, Riemann surfaces with shortest geodesic of maximal length, Geom. Funct. Anal. 3 (1993), no. 6, 564–631.
  • [11] K. Takeuchi, Arithmetic triangle groups, J. Math. Soc. Japan 29 (1977), no. 1, 91–106.
  • [12] K. Takeuchi, A characterization of arithmetic Fuchsian groups, J. Math. Soc. Japan 27 (1975), no. 4, 600–612.
  • [13] M. F. Vignéras, Arithmétique des algèbres de quaternions, Lecture Notes in Math., vol. 800, Springer-Verlag, Berlin, 1980.
  • [14] D. B. Zagier, Zetafunktionen und quadratische Körper, Springer-Verlag, Berlin, 1981.