On the infinite volume Hecke surfaces

Thomas A. Schmidt; Mark Sheingorn

Compositio Mathematica (1995)

  • Volume: 95, Issue: 3, page 247-262
  • ISSN: 0010-437X

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Schmidt, Thomas A., and Sheingorn, Mark. "On the infinite volume Hecke surfaces." Compositio Mathematica 95.3 (1995): 247-262. <http://eudml.org/doc/90349>.

@article{Schmidt1995,
author = {Schmidt, Thomas A., Sheingorn, Mark},
journal = {Compositio Mathematica},
keywords = {length spectrum; Hecke group},
language = {eng},
number = {3},
pages = {247-262},
publisher = {Kluwer Academic Publishers},
title = {On the infinite volume Hecke surfaces},
url = {http://eudml.org/doc/90349},
volume = {95},
year = {1995},
}

TY - JOUR
AU - Schmidt, Thomas A.
AU - Sheingorn, Mark
TI - On the infinite volume Hecke surfaces
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 95
IS - 3
SP - 247
EP - 262
LA - eng
KW - length spectrum; Hecke group
UR - http://eudml.org/doc/90349
ER -

References

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  1. [Be] A. Beardon, The Geometry of Discrete Groups. Graduate Texts in Mathematics 91 (New York: Springer-Verlag) 1983. Zbl0528.30001MR698777
  2. [Bu] P. Buser, Geometry and Spectra of Compact Riemann Surfaces. Progress in Mathematics106 (Boston: Birkhäuser) 1992. Zbl0770.53001MR1183224
  3. [C] C. Croke, Rigidity for surfaces of non-positive curvatures, Comm. Math. Helv.65 (1990) 150-169. Zbl0704.53035MR1036134
  4. [CF] T. Cusick and M. Flahive, The Markoff and Lagrange Spectra, Math. Surveys and Monographs30 (Providence: AMS) 1989. Zbl0685.10023MR1010419
  5. [F] B. Fine, Trace classes and quadratic forms in the modular group, Can. J. Math., to appear. Zbl0814.11026MR1275705
  6. [H] A. Haas, Diophantine approximation on hyperbolic Riemann surfaces, Acta Math.156 (1986) 33-82. Zbl0593.10028MR822330
  7. [H2] A. Haas, Geometric Markoff theory and a theorem of Millington, in: A. Pollington and W. Moran (eds.) Number theory with an emphasis on the Markoff Spectrum (New York: Dekker) (1993) pp. 107-112. Zbl0792.30032MR1219330
  8. [H-S] A. Haas and C. Series, Hurwitz constants and diophantine approximation on Hecke groups, JLMS (2) 34 (1986) 219-234. Zbl0605.10018MR856507
  9. [L] S. Lalley, Mostow rigidity and the Bishop-Steger dichotomy for surfaces of variable negative curvature, Duke Math. J.68 (1992) 237-269. Zbl0782.53032MR1191560
  10. [R] D. Rosen, A class of continued fractions associated with certain properly discontinuous groups, Duke Math. J.21 (1954) 549-563. Zbl0056.30703MR65632
  11. [S-S] T. Schmidt and M. Sheingorn, Length spectra for Hecke triangle surfaces, Math. Z., to appear. Zbl0840.11019MR1362251
  12. [S] M. Sheingorn, Low height Hecke triangle group geodesics, Cont. Math.143 (1993) 545-560. Zbl0792.30034MR1210541
  13. [W] J. Wolfart, Diskrete deformation fuchsscher gruppen und ihrer automorphen formen, J. f.d.r.u.a. Math.348 (1984) 203-220. Zbl0521.10023MR733932

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