Symmetric and asymmetric Diophantine approximation of continued fractions

Jingcheng Tong

Bulletin de la Société Mathématique de France (1989)

  • Volume: 117, Issue: 1, page 59-67
  • ISSN: 0037-9484

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Tong, Jingcheng. "Symmetric and asymmetric Diophantine approximation of continued fractions." Bulletin de la Société Mathématique de France 117.1 (1989): 59-67. <http://eudml.org/doc/87572>.

@article{Tong1989,
author = {Tong, Jingcheng},
journal = {Bulletin de la Société Mathématique de France},
keywords = {symmetric approximation; asymmetric approximation; consecutive convergents; simple continued fraction expansion; symmetric and asymmetric inequalities},
language = {eng},
number = {1},
pages = {59-67},
publisher = {Société mathématique de France},
title = {Symmetric and asymmetric Diophantine approximation of continued fractions},
url = {http://eudml.org/doc/87572},
volume = {117},
year = {1989},
}

TY - JOUR
AU - Tong, Jingcheng
TI - Symmetric and asymmetric Diophantine approximation of continued fractions
JO - Bulletin de la Société Mathématique de France
PY - 1989
PB - Société mathématique de France
VL - 117
IS - 1
SP - 59
EP - 67
LA - eng
KW - symmetric approximation; asymmetric approximation; consecutive convergents; simple continued fraction expansion; symmetric and asymmetric inequalities
UR - http://eudml.org/doc/87572
ER -

References

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  1. [1] BAGEMIHL (F.) and MCLAUGHLIN (J.R.). — Generalization of some classical theorems concerning triples of consecutive convergents to simple continued fractions, J. Reine Angew. Math., t. 221, 1966, p. 146-149. Zbl0135.11104MR32 #1475
  2. [2] BOREL (E.). — Contribution à l'analyse arithmétique du continu, J. Math. Pures Appl., t. 9, 1903, p. 329-375. Zbl34.0239.01JFM34.0239.01
  3. [3] LEJEUNE DIRICHLET (G.P.). — Werke Bd I, II. — Berlin, Reimer 1889, 1897. 
  4. [4] FUJIWARA (M.). — Bemerkung zur Theorie der Approximation der irrationalen Zahlen durch rationale Zahlen, Tôhoku Math. J., t. 14, 1918, p. 109-115. JFM46.0278.05
  5. [5] HURWITZ (A.). — Über die angenäherte Darstellung der irrationalzahlen durch rationale Brüche, Math. Ann., t. 39, 1891, p. 279-284. JFM23.0222.02
  6. [6] LEVEQUE (W.J.). — On asymmetric approximations, Michigan Math. J., t. 2, 1953, p. 1-6. Zbl0059.03901MR16,18b
  7. [7] MÜLLER (M.). — Über die Approximation reeller Zahlen durch die Näherungsbrüche ihres regelmässigen Kettenbruches, Arch. Math., t. 6, 1955, p. 253-258. Zbl0064.04401
  8. [8] PERRON (O.). — Die Lehre von den Kettenbrüchen I, II. — Leipzig, 3rd ed. Teubner, 1954. 
  9. [9] ROBINSON (R.M.). — Unsymmetric approximation of irrational numbers, Bull. Amer. Math. Soc., t. 53, 1947, p. 351-361. Zbl0032.40003MR8,566b
  10. [10] SEGRE (B.). — Lattice points in infinite domains and asymmetric Diophantine approximation, Duke Math. J., t. 12, 1945, p. 337-365. Zbl0060.11807MR6,258a
  11. [11] SZÜSZ (P.). — On a theorem of Segre, Acta Arith., t. 23, 1973, p. 371-377. Zbl0236.10018MR49 #8942
  12. [12] TONG (J.). — The conjugate property of the Borel theorem on Diophantine approximation, Math. Z., t. 184, 1983, p. 151-153. Zbl0497.10024MR85m:11039
  13. [13] TONG (J.). — On two theorems of Kopetzky and Schnitzer on the approximation of continued fractions, J. Reine Angew. Math., t. 362, 1985, p. 1-3. Zbl0568.10019MR87g:11081
  14. [14] TONG (J.). — A theorem on approximation of irrational numbers by simple continued fractions, Proc. Edinburgh Math. Soc., t. 31, 1988, p. 197-204. Zbl0645.10008MR90e:11101
  15. [15] TONG (J.). — Segre's theorem on asymmetric Diophantine approximation, J. Number Theory, t. 28, 1988, p. 116-118. Zbl0645.10009MR89h:11033

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