Skip to main content
Log in

On a lattice-point problem in hyperbolic space and related questions in spectral theory

  • Published:
Arkiv för Matematik

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Colin de Verdiere, Y., Théorie spectrale des surfaces de Riemann d’aire infinie.Astérisque 132 (1985), 259–275.

    MathSciNet  Google Scholar 

  2. Lax, P. andPhillips, R. S., The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces.J. Funct. Anal. 46 (1982), 280–350.

    Article  MATH  MathSciNet  Google Scholar 

  3. Mazzeo, R. R. andMelrose, R. B., Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature.Preprint, 1986.

  4. Nicholls, P. J. A lattice point problem in hyperbolic space.Michigan Math. J. 30 (1982), 273–287.

    MathSciNet  Google Scholar 

  5. Patterson, S. J., The limit set of a Fuchsian group.Acta Math. 136 (1976), 241–273.

    Article  MATH  MathSciNet  Google Scholar 

  6. Patterson, S. J., Spectral theory and Fuchsian groups,Math. Proc. Cambridge Philos. Soc. 81 (1977), 59–75.

    MATH  MathSciNet  Google Scholar 

  7. Patterson, S. J., Lectures on measures on limit sets of Kleinian groups.Analytic and geometric aspects of hyperbolic space, Warwick and Durham, 1984, Ed. Epstein, D. B. A., Cambridge Univ. Press, 1986.

  8. Parry, W. andPollicot, M., An analogue of the prime number theorem for closed orbits of Axiom A flows.Ann. of Math. 118 (1983), 573–591.

    Article  MathSciNet  Google Scholar 

  9. Ruelle, D., Repellers for real analytic maps.Ergodic Theory and Dynamical Systems 2 (1982), 99–107.

    Article  MATH  MathSciNet  Google Scholar 

  10. Sullivan, D., The density at infinity of a discrete group of hyperbolic motions.Inst. Hautes Études Sci. Publ. Math. 50 (1979), 419–450.

    Article  Google Scholar 

  11. Sullivan, D., Discrete conformal groups and measurable dynamics,Bull. Amer. Math. Soc. 6 (1982), 57–73.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Patterson, S.J. On a lattice-point problem in hyperbolic space and related questions in spectral theory. Ark. Mat. 26, 167–172 (1988). https://doi.org/10.1007/BF02386116

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02386116

Keywords

Navigation