ArticleOriginal scientific text

Title

Metric properties of some special p-adic series expansions

Authors 1, 2

Affiliations

  1. Department of Computational & Applied Mathematics, University of the Witwatersrand, Johannesburg, 2050, South Africa
  2. Department of Mathematics, University of the Witwatersrand, Johannesburg, 2050, South Africa

Bibliography

  1. J. Barrionuevo, R. M. Burton, K. Dajani and C. Kraaikamp, Ergodic properties of generalized Lüroth series, Acta Arith. 74 (1996), 311-327.
  2. P. Billingsley, Ergodic Theory and Information, Wiley, 1965.
  3. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd ed., Wiley, 1968.
  4. J. Galambos, Representations of Real Numbers by Infinite Series, Springer, 1976.
  5. H. Jager and C. de Vroedt, Lüroth series and their ergodic properties, Nederl. Akad. Wetensch. Proc. Ser. A 72 (1969), 31-42.
  6. A. Y. Khintchine, Metrische Kettenbruchprobleme, Compositio Math. 1 (1935), 361-382.
  7. A. Knopfmacher and J. Knopfmacher, Series expansions in p-adic and other non-archimedean fields, J. Number Theory 32 (1989), 297-306.
  8. A. Knopfmacher and J. Knopfmacher, Infinite series expansions for p-adic numbers, J. Number Theory 41 (1992), 131-145.
  9. A. Knopfmacher and J. Knopfmacher, Metric properties of algorithms inducing Lüroth series expansions of Laurent series, Astérisque 209 (1992), 237-246.
  10. J. Knopfmacher, Ergodic properties of some inverse polynomial series expansions of Laurent series, Acta Math. Hungar. 60 (1992), 241-246.
  11. K. Knopp, Theory and Application of Infinite Series, Dover, 1990.
  12. N. Koblitz, p-adic Numbers, p-adic Analysis, and Zeta-Functions, 2nd ed., Springer, 1984.
  13. Y. Laohakosol, A characterization of p-adic Ruban continued fractions, J. Austral. Math. Soc. A 39 (1985), 300-305.
  14. K. Mahler, Zur Approximation p-adischer Irrationalzahlen, Nieuw Arch. Wisk. 18 (1934), 22-34.
  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.
  16. O. Perron, Irrationalzahlen, Chelsea, 1951.
  17. A. A. Ruban, Some metric properties of p-adic numbers, Siberian Math. J. 11 (1970), 176-180.
  18. T. Salát, Zur metrischen Theorie der Lürothschen Entwicklungen der reellen Zahlen, Czechoslovak Math. J. 18 (1968), 489-522.
  19. W. H. Schikhof, Ultrametric Calculus, Cambridge University Press, 1984.
  20. V. G. Sprindžuk, Mahler's Problem in Metric Number Theory, Amer. Math. Soc., 1969.
Pages:
11-19
Main language of publication
English
Received
1994-12-01
Accepted
1995-07-18
Published
1996
Exact and natural sciences