Metric properties of some special p-adic series expansions

 Access to full text

 Full (PDF)

1. [1] J. Barrionuevo, R. M. Burton, K. Dajani and C. Kraaikamp, Ergodic properties of generalized Lüroth series, Acta Arith. 74 (1996), 311-327. Zbl0848.11039
2. [2] P. Billingsley, Ergodic Theory and Information, Wiley, 1965. Zbl0141.16702
3. [3] W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd ed., Wiley, 1968. Zbl0155.23101
4. [4] J. Galambos, Representations of Real Numbers by Infinite Series, Springer, 1976. 
5. [5] H. Jager and C. de Vroedt, Lüroth series and their ergodic properties, Nederl. Akad. Wetensch. Proc. Ser. A 72 (1969), 31-42. Zbl0167.32201
6. [6] A. Y. Khintchine, Metrische Kettenbruchprobleme, Compositio Math. 1 (1935), 361-382. 
7. [7] A. Knopfmacher and J. Knopfmacher, Series expansions in p-adic and other non-archimedean fields, J. Number Theory 32 (1989), 297-306. Zbl0683.10030
8. [8] A. Knopfmacher and J. Knopfmacher, Infinite series expansions for p-adic numbers, J. Number Theory 41 (1992), 131-145. Zbl0756.11021
9. [9] A. Knopfmacher and J. Knopfmacher, Metric properties of algorithms inducing Lüroth series expansions of Laurent series, Astérisque 209 (1992), 237-246. Zbl0788.11031
10. [10] J. Knopfmacher, Ergodic properties of some inverse polynomial series expansions of Laurent series, Acta Math. Hungar. 60 (1992), 241-246. Zbl0774.11073
11. [11] K. Knopp, Theory and Application of Infinite Series, Dover, 1990. 
12. [12] N. Koblitz, p-adic Numbers, p-adic Analysis, and Zeta-Functions, 2nd ed., Springer, 1984. Zbl0364.12015
13. [13] Y. Laohakosol, A characterization of p-adic Ruban continued fractions, J. Austral. Math. Soc. A 39 (1985), 300-305. Zbl0582.10021
14. [14] K. Mahler, Zur Approximation p-adischer Irrationalzahlen, Nieuw Arch. Wisk. 18 (1934), 22-34. Zbl60.0163.02
15. [15] 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. Zbl0254.10046
16. [16] O. Perron, Irrationalzahlen, Chelsea, 1951. 
17. [17] A. A. Ruban, Some metric properties of p-adic numbers, Siberian Math. J. 11 (1970), 176-180. Zbl0213.32701
18. [18] T. Salát, Zur metrischen Theorie der Lürothschen Entwicklungen der reellen Zahlen, Czechoslovak Math. J. 18 (1968), 489-522. Zbl0162.34703
19. [19] W. H. Schikhof, Ultrametric Calculus, Cambridge University Press, 1984. 
20. [20] V. G. Sprindžuk, Mahler's Problem in Metric Number Theory, Amer. Math. Soc., 1969.