Symmetric and asymmetric Diophantine approximation of continued fractions
Bulletin de la Société Mathématique de France, Volume 117 (1989) no. 1, pp. 59-67.
@article{BSMF_1989__117_1_59_0,
     author = {Tong, Jingcheng},
     title = {Symmetric and asymmetric {Diophantine} approximation of continued fractions},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {59--67},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {117},
     number = {1},
     year = {1989},
     doi = {10.24033/bsmf.2112},
     mrnumber = {90k:11086},
     zbl = {0684.10030},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/bsmf.2112/}
}
TY  - JOUR
AU  - Tong, Jingcheng
TI  - Symmetric and asymmetric Diophantine approximation of continued fractions
JO  - Bulletin de la Société Mathématique de France
PY  - 1989
SP  - 59
EP  - 67
VL  - 117
IS  - 1
PB  - Société mathématique de France
UR  - http://www.numdam.org/articles/10.24033/bsmf.2112/
DO  - 10.24033/bsmf.2112
LA  - en
ID  - BSMF_1989__117_1_59_0
ER  - 
%0 Journal Article
%A Tong, Jingcheng
%T Symmetric and asymmetric Diophantine approximation of continued fractions
%J Bulletin de la Société Mathématique de France
%D 1989
%P 59-67
%V 117
%N 1
%I Société mathématique de France
%U http://www.numdam.org/articles/10.24033/bsmf.2112/
%R 10.24033/bsmf.2112
%G en
%F BSMF_1989__117_1_59_0
Tong, Jingcheng. Symmetric and asymmetric Diophantine approximation of continued fractions. Bulletin de la Société Mathématique de France, Volume 117 (1989) no. 1, pp. 59-67. doi : 10.24033/bsmf.2112. http://www.numdam.org/articles/10.24033/bsmf.2112/

[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. | MR | Zbl

[2] Borel (E.). - Contribution à l'analyse arithmétique du continu, J. Math. Pures Appl., t. 9, 1903, p. 329-375. | JFM | Numdam

[3] Lejeune Dirichlet (G.P.). - Werke Bd I, II. - Berlin, Reimer 1889, 1897.

[4] Fujiwara (M.). - Bemerkung zur Theorie der Approximation der irrationalen Zahlen durch rationale Zahlen, Tôhoku Math. J., t. 14, 1918, p. 109-115. | JFM

[5] Hurwitz (A.). - Über die angenäherte Darstellung der irrationalzahlen durch rationale Brüche, Math. Ann., t. 39, 1891, p. 279-284. | JFM

[6] Leveque (W.J.). - On asymmetric approximations, Michigan Math. J., t. 2, 1953, p. 1-6. | MR | Zbl

[7] Müller (M.). - Über die Approximation reeller Zahlen durch die Näherungsbrüche ihres regelmässigen Kettenbruches, Arch. Math., t. 6, 1955, p. 253-258. | Zbl

[8] Perron (O.). - Die Lehre von den Kettenbrüchen I, II. - Leipzig, 3rd ed. Teubner, 1954.

[9] Robinson (R.M.). - Unsymmetric approximation of irrational numbers, Bull. Amer. Math. Soc., t. 53, 1947, p. 351-361. | MR | Zbl

[10] Segre (B.). - Lattice points in infinite domains and asymmetric Diophantine approximation, Duke Math. J., t. 12, 1945, p. 337-365. | MR | Zbl

[11] Szüsz (P.). - On a theorem of Segre, Acta Arith., t. 23, 1973, p. 371-377. | MR | Zbl

[12] Tong (J.). - The conjugate property of the Borel theorem on Diophantine approximation, Math. Z., t. 184, 1983, p. 151-153. | MR | Zbl

[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. | MR | Zbl

[14] Tong (J.). - A theorem on approximation of irrational numbers by simple continued fractions, Proc. Edinburgh Math. Soc., t. 31, 1988, p. 197-204. | MR | Zbl

[15] Tong (J.). - Segre's theorem on asymmetric Diophantine approximation, J. Number Theory, t. 28, 1988, p. 116-118. | MR | Zbl

Cited by Sources: