Distribution of Lévy constants for quadratic numbers

Christian Faivre

Acta Arithmetica (1992)

  • Volume: 61, Issue: 1, page 13-34
  • ISSN: 0065-1036

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Christian Faivre. "Distribution of Lévy constants for quadratic numbers." Acta Arithmetica 61.1 (1992): 13-34. <http://eudml.org/doc/206448>.

@article{ChristianFaivre1992,
author = {Christian Faivre},
journal = {Acta Arithmetica},
keywords = {Lévy type theorems; regular continued fraction expansion; quadratic irrationality; Lévy constant},
language = {eng},
number = {1},
pages = {13-34},
title = {Distribution of Lévy constants for quadratic numbers},
url = {http://eudml.org/doc/206448},
volume = {61},
year = {1992},
}

TY - JOUR
AU - Christian Faivre
TI - Distribution of Lévy constants for quadratic numbers
JO - Acta Arithmetica
PY - 1992
VL - 61
IS - 1
SP - 13
EP - 34
LA - eng
KW - Lévy type theorems; regular continued fraction expansion; quadratic irrationality; Lévy constant
UR - http://eudml.org/doc/206448
ER -

References

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  3. [3] C. Faivre, Distribution des constantes de Lévy des nombres quadratiques, Ph.D. Thesis, Université de Provence, 1990. 
  4. [4] E. Galois, Démonstration d'un théorème sur les fractions continues périodiques, Ann. Math. Pures Appl. 19 (1828-1829), 294-301. Zbl61.0227.02
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  9. [9] H. Jager et P. Liardet, Distributions arithmétiques des dénominateurs des convergents de fractions continues, Indag. Math. 50 (1988), 181-197. Zbl0655.10045
  10. [10] N. V. Kuznetsov, The distribution of norms of primitive hyperbolic classes of the modular group, Soviet Math. Dokl. 19 (5) (1978), 1053-1056. Zbl0419.10030
  11. [11] E. Landau, Elementary Number Theory, Chelsea, New York 1958. 
  12. [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. Zbl55.0916.02
  13. [13] D. Mayer, On a ζ function related to the continued fraction transformation, Bull. Soc. Math. France 104 (1976), 195-203. Zbl0328.58011
  14. [14] M. Pollicott, Distribution of closed geodesics on the modular surface and quadratic irrationals, Bull. Soc. Math. France 144 (1986), 431-446. Zbl0624.58019
  15. [15] D. Ruelle, Zeta-functions for expanding maps and Anosov flows, Invent. Math. 34 (1976), 231-242. Zbl0329.58014
  16. [16] P. Sarnak, Class numbers of indefinite binary quadratic forms, J. Number Theory 15 (1982), 229-247. Zbl0499.10021
  17. [17] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Publ. Math. Soc. Japan 11, Iwanami Shoten and Princeton University Press, 1971. Zbl0221.10029
  18. [18] Y.-T. Siu, Techniques of Extension of Analytic Objects, Lectures Notes in Pure and Appl. Math. 8, Dekker, 1974. 
  19. [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. 

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