Metric properties of algorithms inducing Lüroth series expansions of Laurent series
Journées arithmétiques de Genève - 9-13 septembre 1991, Astérisque no. 209  (1992), p. 237-246
@incollection{AST_1992__209__237_0,
     author = {Knopfmacher, John and Knopfmacher, Arnold},
     title = {Metric properties of algorithms inducing L\"uroth series expansions of Laurent series},
     booktitle = {Journ\'ees arithm\'etiques de Gen\`eve - 9-13 septembre 1991},
     editor = {Coray D. F. and P\'etermann Y.-F. S},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {209},
     year = {1992},
     pages = {237-246},
     zbl = {0788.11031},
     mrnumber = {1211017},
     language = {en},
     url = {http://www.numdam.org/item/AST_1992__209__237_0}
}
Knopfmacher, John; Knopfmacher, Arnold. Metric properties of algorithms inducing Lüroth series expansions of Laurent series, in Journées arithmétiques de Genève - 9-13 septembre 1991, Astérisque, no. 209 (1992), pp. 237-246. http://www.numdam.org/item/AST_1992__209__237_0/

[1] E. Artin, Quadratische Körper im Gebiete der höheren Kongruenzen, I-II. Math. Z. 19 (1924), 153-246. | Article | JFM 51.0144.05 | MR 1544651

[2] W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1 (3rd Ed.). J. Wiley, 1968. | MR 228020 | Zbl 0155.23101

[3] J. Galambos, Representations of Real Numbers by Infinite Series. Springer-Verlag, 1976. | Article | MR 568141 | Zbl 0322.10002

[4] D. R. Hayes, Real quadratic function fields. Canadian Math. Soc. Conf. Proceedings, 7 (1987), 203-236. | MR 894324 | Zbl 0664.12011

[5] H. Jager and C. De Vroedt, Lüroth series and their ergodic properties. Proc. K. Nederl. Akad. Wet., A 72 (1969), 31-42. | MR 238793 | Zbl 0167.32201

[6] W. B. Jones and W. J. Thron, Continued Fractions. Addison-Wesley, 1980. | MR 595864 | Zbl 0445.30003

[7] A. Y. Khintchine, Metrische Kettenbruchprobleme, Compositio Math., 1 (1935), 361-382. | JFM 60.0948.04 | Numdam | MR 1556899 | Zbl 0010.34101

[8] A. Knopfmacher and J. Knopfmacher, Inverse polynomial expansions of Laurent series, I-II. Constr. Approx., 4 (1988), 379-389, and | Article | MR 956174 | Zbl 0659.41024

A. Knopfmacher and J. Knopfmacher, Inverse polynomial expansions of Laurent series, I-II J. Comp. Appl. Math., 28 (1989), 249-257. | Article | MR 1038848 | Zbl 0684.30030

[9] J. Knopfmacher, Ergodic properties of some inverse polynomial series expansions of Laurent series; accepted by Acta Math. Hungarica. | MR 1177678 | Zbl 0774.11073

[10] K. Knopp, Theory & Application of Infinite Series, Dover, 1990. | Zbl 0042.29203

[11] A. Magnus, Certain continued fractions associated with the Padé table. Math. Z., 78 (1962), 361-374. | Article | MR 150271 | Zbl 0104.05102

[12] A. Magnus, p-fractions and the Padé table. Rocky Mtn. J. Math., 4 (1974), 257-259. | Article | MR 342915 | Zbl 0293.41016

[13] R. Paysant-Le Roux and E. Dubois, Algorithme de Jacobi-Perron dans un corps de séries formelles. C.R. Acad. Sci. Paris, A 272 (1971), 564-566. | MR 285481 | Zbl 0213.06301

[14] R. Paysant-Le Roux and E. Dubois, Étude métrique de l'algorithme de Jacobi-Perron dans un corps de séries formelles. C.R. Acad. Sci. Paris, A 275 (1972), 683-686. | MR 311582 | Zbl 0254.10046

[15] O. Perron, Irrationalzahlen. Chelsea Publ. Co., 1951. | MR 115985

[16] T. Salát, Zur Metrischen Theorie der Lüroschen Entwicklungen der reellen Zahlen, Czech. Math. J., 18 (1968), 489-522. | MR 229605 | Zbl 0162.34703

[17] V. G. Sprindžuk, Mahler's Problem in Metrie Number Theory. American Math. Soc., 1969. | MR 245527 | Zbl 0181.05502