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Systoles of arithmetic surfaces and the Markoff spectrum

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References

  1. A. Baragar: Integral solutions of Markoff-Hurwitz equations. J. Number Theory49 (1994), 27–44

    Google Scholar 

  2. J. Cassels: An introduction to Diophantine approximation. Cambridge University Press, Cambridge (1959)

    Google Scholar 

  3. H. Cohn: Approach to Markoff's minimal forms through modular functions. Annals of Math.61 (1955), 1–12

    Google Scholar 

  4. H. Cohn: Representation of Markoff's minimal forms by geodesics on a perforated torus. Acta Arith.18 (1971), 125–136

    Google Scholar 

  5. T. Cusick, M. Flahive: The Markoff and Lagrange Spectra. Math. Surveys, vol. 30, AMS Providence (1989)

  6. L. Dickson: Studies in the theory of numbers. Univ. Press Chicago (1930)

  7. G. Frobenius: Ueber die Markoffschen Zahlen. Gesammelte Abhandlungen, Bd. 3, Springer, Berlin Heidelberg New York (1968), 598–627

    Google Scholar 

  8. A. Haas: Diophantine approximation on hyperbolic Riemann surfaces. Acta Math.156 (1986), 33–82

    Google Scholar 

  9. J. Lehner, M. Sheingorn: Simple closed geodesics on Γ(3) arise from the Markoff spectrum. Bulletin AMS11 (1984), 359–362

    Google Scholar 

  10. A. Markoff: Sur les formes binaires indéfinies. Math. Annalen15 (1879), 381–406

    Google Scholar 

  11. A. Markoff: Sur les formes binaires indéfinies (Second mémoire). Math. Annalen17 (1880), 379–399

    Google Scholar 

  12. G. Mathews: Theory of numbers. Second ed. Chelsea Publishing Company, New York (1961)

    Google Scholar 

  13. A. Pollington, W. Moran: Number theory with an emphasis on the Markoff spectrum. Marcel Dekker New York Basel Hongkong (1993)

    Google Scholar 

  14. T. Schmidt, M. Sheingorn: On the infinite volume Hecke surfaces. Compositio Math.95 (1995), 247–262

    Google Scholar 

  15. P. Schmutz: Arithmetic Fuchsian groups and the number of systoles. To appear in Math. ZV.

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Schmutz, P. Systoles of arithmetic surfaces and the Markoff spectrum. Math. Ann. 305, 191–203 (1996). https://doi.org/10.1007/BF01444218

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  • DOI: https://doi.org/10.1007/BF01444218

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