The Thermodynamic Formalism Approach to Selberg's Zeta Function for Psl(2, Z)

@inproceedings{Mayer1991TheTF,
  title={The Thermodynamic Formalism Approach to Selberg's Zeta Function for Psl(2, Z)},
  author={Dieter Mayer},
  year={1991}
}
Besides the classical approach to Selberg's zeta function for cofinite Fuchsian groups [S] through the trace formula [V] there has been developed recently another one based on the thermodynamic formalism [R2] applied to the dynamical zeta function of Smale and Ruelle [F] which for geodesic flows on surfaces of constant negative curvature (c.n.c.) is closely related to Selberg's function for the corresponding Fuchsian group [Sm, Rl]. This latter approach however has been worked out up to now… CONTINUE READING
Highly Cited
This paper has 24 citations. REVIEW CITATIONS

References

Publications referenced by this paper.
Showing 1-8 of 8 references

Pollicott, Distribution of closed geodesies on the modular surface and quadratic irrationals

  • M. Pol
  • Bull. Soc. Math. France
  • 1986

The zeta functions of Ruelle and Selberg

  • D. Fried
  • I, Ann. Sci. École Norm. Sup
  • 1986

An analogue of the prime number theorem for closed orbits of shifts of finite type and their suspensions, Israel

  • W. Parry
  • J. Math
  • 1983

The Ruelle-Araki transfer operator in classical statistical mechanics

  • D. Mayer
  • Lecture Notes in Phys.,
  • 1980

Series, Markov maps associated to Fuchsian groups, Inst

  • C. R. Bowen
  • Hautes Études Sci. Publ. Math
  • 1979

Spectral theory of automorphic functions, the Selberg zeta function, and some problems of analytic number theory and mathematical physics, Russian Math. Surveys

  • A. B. Venkov
  • 1979

Ein mechanisches System mit quasi-ergodischen Bahnen

  • E. Artin
  • Collected Papers, Addison-Wesley,
  • 1965

Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series

  • A. Selberg
  • J. Indian Math. Soc
  • 1956

Similar Papers

Loading similar papers…