On a theorem of Legendre in the theory of continued fractions

Dominique Barbolosi; Hendrik Jager

Journal de théorie des nombres de Bordeaux (1994)

  • Volume: 6, Issue: 1, page 81-94
  • ISSN: 1246-7405

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Barbolosi, Dominique, and Jager, Hendrik. "On a theorem of Legendre in the theory of continued fractions." Journal de théorie des nombres de Bordeaux 6.1 (1994): 81-94. <http://eudml.org/doc/247535>.

@article{Barbolosi1994,
author = {Barbolosi, Dominique, Jager, Hendrik},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {approximation coefficient of a rational number; analogues of Legendre's theorem; continued fractions},
language = {eng},
number = {1},
pages = {81-94},
publisher = {Université Bordeaux I},
title = {On a theorem of Legendre in the theory of continued fractions},
url = {http://eudml.org/doc/247535},
volume = {6},
year = {1994},
}

TY - JOUR
AU - Barbolosi, Dominique
AU - Jager, Hendrik
TI - On a theorem of Legendre in the theory of continued fractions
JO - Journal de théorie des nombres de Bordeaux
PY - 1994
PB - Université Bordeaux I
VL - 6
IS - 1
SP - 81
EP - 94
LA - eng
KW - approximation coefficient of a rational number; analogues of Legendre's theorem; continued fractions
UR - http://eudml.org/doc/247535
ER -

References

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  1. [1] D. Barbolosi, Fractions continues à quotients partiels impairs, Thèse, Université de Provence, Marseille (1988). Zbl0713.11052
  2. [2] P. Billingsley, Ergodic Theory and Information, John Wiley and Sons, New York, London, Sydney (1965). Zbl0141.16702MR192027
  3. [3] W. Bosma, H. Jager and F. Wiedijk, Some metrical observations on the approximation by continued fractions, Indag. Math.4 (1983), 281-299. Zbl0519.10043MR718069
  4. [4] P. Fatou, Sur l'approximation des incommensurables et les séries trigonométriques, C. R. Acad. Sci. Paris139 (1904), 1019-1021. Zbl35.0275.02JFM35.0275.02
  5. [5] J.H. Grace, The classification of rational approximations, Proc. London Math. Soc.17 (1918), 247-258. Zbl47.0166.01JFM47.0166.01
  6. [6] S. Ito and H. Nakada, On natural extensions of transformations related to Diophantine approximations, Proceedings of the Conference on Number Theory and Combinatorics, Japan 1984, World Scientific Publ. Co., Singapore (1985), 185-207. Zbl0623.10008MR827784
  7. [7] S. Ito, On Legendre's Theorem related to Diophantine approximations, Séminaire de Théorie des Nombres, Bordeaux, exposé 44 (1987-1988), 44-01-44-19. Zbl0714.11037
  8. [8] H. Jager and C. Kraaikamp, On the approximation by continued fractions, Indag. Math.51 (1989), 289-307. Zbl0695.10029MR1020023
  9. [9] J.F. Koksma, Diophantische Approximationen, Julius Springer, Berlin (1936). Zbl0012.39602MR344200
  10. [10] J.F. Koksma, Bewijs van een stelling over kettingbreuken, Mathematica A6 (1937),226-231. Zbl0018.05302JFM63.0923.02
  11. [11] J.F. Koksma, On continued fractions, Simon Stevin29 (1951/52), 96-102. Zbl0047.28302MR50640
  12. [12] C. Kraaikamp, A new class of continued fractions, Acta Arith.57 (1991), 1-39. Zbl0721.11029MR1093246
  13. [13] A.M. Legendre, Essai sur la théorie des nombres, Duprat, Paris, An VI (1798). JFM30.0201.03
  14. [14] F. Schweiger, On the approximation by continued fractions with odd and even partial quotients, Mathematisches Institut der Universität Salzburg, Arbeitsbericht1-2 (1984), 105-114. 

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