@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}, zbl = {0684.10030}, mrnumber = {90k:11086}, language = {en}, url = {http://archive.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 DA - 1989/// SP - 59 EP - 67 VL - 117 IS - 1 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/bsmf.2112/ UR - https://zbmath.org/?q=an%3A0684.10030 UR - https://www.ams.org/mathscinet-getitem?mr=90k:11086 UR - https://doi.org/10.24033/bsmf.2112 DO - 10.24033/bsmf.2112 LA - en ID - BSMF_1989__117_1_59_0 ER -
Tong, Jingcheng. Symmetric and asymmetric Diophantine approximation of continued fractions. Bulletin de la Société Mathématique de France, Tome 117 (1989) no. 1, pp. 59-67. doi : 10.24033/bsmf.2112. http://archive.numdam.org/articles/10.24033/bsmf.2112/
[1] 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 32 #1475 | Zbl 0135.11104
and . -[2] Contribution à l'analyse arithmétique du continu, J. Math. Pures Appl., t. 9, 1903, p. 329-375. | JFM 34.0239.01
. -[3] Werke Bd I, II. - Berlin, Reimer 1889, 1897.
. -[4] Bemerkung zur Theorie der Approximation der irrationalen Zahlen durch rationale Zahlen, Tôhoku Math. J., t. 14, 1918, p. 109-115. | JFM 46.0278.05
. -[5] Über die angenäherte Darstellung der irrationalzahlen durch rationale Brüche, Math. Ann., t. 39, 1891, p. 279-284. | JFM 23.0222.02
. -[6] On asymmetric approximations, Michigan Math. J., t. 2, 1953, p. 1-6. | MR 16,18b | Zbl 0059.03901
. -[7] Über die Approximation reeller Zahlen durch die Näherungsbrüche ihres regelmässigen Kettenbruches, Arch. Math., t. 6, 1955, p. 253-258. | Zbl 0064.04401
. -[8] Die Lehre von den Kettenbrüchen I, II. - Leipzig, 3rd ed. Teubner, 1954.
. -[9] Unsymmetric approximation of irrational numbers, Bull. Amer. Math. Soc., t. 53, 1947, p. 351-361. | MR 8,566b | Zbl 0032.40003
. -[10] Lattice points in infinite domains and asymmetric Diophantine approximation, Duke Math. J., t. 12, 1945, p. 337-365. | MR 6,258a | Zbl 0060.11807
. -[11] On a theorem of Segre, Acta Arith., t. 23, 1973, p. 371-377. | MR 49 #8942 | Zbl 0236.10018
. -[12] The conjugate property of the Borel theorem on Diophantine approximation, Math. Z., t. 184, 1983, p. 151-153. | MR 85m:11039 | Zbl 0497.10024
. -[13] On two theorems of Kopetzky and Schnitzer on the approximation of continued fractions, J. Reine Angew. Math., t. 362, 1985, p. 1-3. | MR 87g:11081 | Zbl 0568.10019
. -[14] A theorem on approximation of irrational numbers by simple continued fractions, Proc. Edinburgh Math. Soc., t. 31, 1988, p. 197-204. | MR 90e:11101 | Zbl 0645.10008
. -[15] Segre's theorem on asymmetric Diophantine approximation, J. Number Theory, t. 28, 1988, p. 116-118. | MR 89h:11033 | Zbl 0645.10009
. -Cité par Sources :