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ArticleOriginal scientific text

Title

Distribution of Lévy constants for quadratic numbers

Authors 1

Affiliations

  1. URA 225 Université de Provence, U.F.R.-M.I.M., 3, Place Victor Hugo, 13331 Marseille Cedex 3, France

Bibliography

  1. P. Billingsley, Ergodic Theory and Information, Wiley, New York 1965.
  2. N. Dunford and J. Schwartz, Linear Operators, Part I, Wiley-Interscience, 1963.
  3. C. Faivre, Distribution des constantes de Lévy des nombres quadratiques, Ph.D. Thesis, Université de Provence, 1990.
  4. E. Galois, Démonstration d'un théorème sur les fractions continues périodiques, Ann. Math. Pures Appl. 19 (1828-1829), 294-301.
  5. A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  6. A. Grothendieck, La théorie de Fredholm, Bull. Soc. Math. France 84 (1956), 319-384.
  7. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Clarendon Press, Oxford 1968.
  8. D. Hejhal, The Selberg Trace Formula for PSL(2,ℝ), Vol. 2, Lecture Notes in Math. 1001, Springer, 1983.
  9. H. Jager et P. Liardet, Distributions arithmétiques des dénominateurs des convergents de fractions continues, Indag. Math. 50 (1988), 181-197.
  10. N. V. Kuznetsov, The distribution of norms of primitive hyperbolic classes of the modular group, Soviet Math. Dokl. 19 (5) (1978), 1053-1056.
  11. E. Landau, Elementary Number Theory, Chelsea, New York 1958.
  12. P. Lévy, Sur les lois de probabilités dont dépendent les quotients complets et incomplets d'une fraction continue, Bull. Soc. Math. France 57 (1929), 178-194.
  13. D. Mayer, On a ζ function related to the continued fraction transformation, Bull. Soc. Math. France 104 (1976), 195-203.
  14. M. Pollicott, Distribution of closed geodesics on the modular surface and quadratic irrationals, Bull. Soc. Math. France 144 (1986), 431-446.
  15. D. Ruelle, Zeta-functions for expanding maps and Anosov flows, Invent. Math. 34 (1976), 231-242.
  16. P. Sarnak, Class numbers of indefinite binary quadratic forms, J. Number Theory 15 (1982), 229-247.
  17. G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Publ. Math. Soc. Japan 11, Iwanami Shoten and Princeton University Press, 1971.
  18. Y.-T. Siu, Techniques of Extension of Analytic Objects, Lectures Notes in Pure and Appl. Math. 8, Dekker, 1974.
  19. H. Smith, Note on the theory of the Pellian equation, and of binary quadratic forms of a positive determinant, Proc. London Math. Soc. 7 (1876), 199-208.
Acta Arithmetica
1992/61/1
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Pages:
13-34
Main language of publication
English
Received
1990-07-10
Accepted
1991-06-05
Published
1992
Exact and natural sciences