manuscripta mathematica

, Volume 67, Issue 1, pp 187–195

Sur le developpement de\(\sqrt m\) en fraction continue p-adiqueen fraction continue p-adique

  • Edmondo Bedocchi
Article
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Abstract

This note deals with the Mahler-Browkin p-adic continued fractions. The principal result is the following:

For any prime p>2 and for any d ∈ ℕ, d odd, there are only finitely many m ∈ ℤ such that the p-adic continued fraction expansion of\(\sqrt m\) ∈ ℚp is periodic with period of length d.

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Bibliographie

  1. [1]
    BEDOCCHI, E.: Nota sulle frazioni continue p-adiche. Ann. Mat. Pura Appl.152, 197–207 (1988)MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    BEDOCCHI, E.: Remarks on periods of p-adic continued fractions. Boll. Un. Mat. Ital. (7)3-A, 209–214 (1989)MathSciNetGoogle Scholar
  3. [3]
    BROWKIN, J.: Continued fractions in local fields I. Demonstratio Math.11, 67–82 (1978)MATHMathSciNetGoogle Scholar
  4. [4]
    MAHLER, K.: Zur Approximation p-adischer Irrationalzahlen. Nieuw Arch. Wisk.18, 22–34 (1936)Google Scholar
  5. [5]
    SIERPINSKI, W.: Elementary Theory of Numbers. Amsterdam & Warszawa: North Holland & PWN 1988MATHGoogle Scholar
  6. [6]
    TILBORGHS, F.: Periodic p-adic continued fractions. Faculty of Applied Sciences Free University of Brussels VUB, 1–12 (1989)Google Scholar
  7. [7]
    de WEGER, B.M.M.: Approximation lattices of p-adic numbers. J. Number Theory24, 70–88 (1986)MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    de WEGER, B.M.M.: Periodicity of p-adic continued fractions. Elem. Math.43, 112–116 (1988)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Edmondo Bedocchi
    • 1
  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItalia

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