Skip to main content
SpringerLink
Log in

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

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Bibliographie

  1. BEDOCCHI, E.: Nota sulle frazioni continue p-adiche. Ann. Mat. Pura Appl.152, 197–207 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  2. BEDOCCHI, E.: Remarks on periods of p-adic continued fractions. Boll. Un. Mat. Ital. (7)3-A, 209–214 (1989)

    MathSciNet  Google Scholar 

  3. BROWKIN, J.: Continued fractions in local fields I. Demonstratio Math.11, 67–82 (1978)

    MATH  MathSciNet  Google Scholar 

  4. MAHLER, K.: Zur Approximation p-adischer Irrationalzahlen. Nieuw Arch. Wisk.18, 22–34 (1936)

    Google Scholar 

  5. SIERPINSKI, W.: Elementary Theory of Numbers. Amsterdam & Warszawa: North Holland & PWN 1988

    MATH  Google Scholar 

  6. TILBORGHS, F.: Periodic p-adic continued fractions. Faculty of Applied Sciences Free University of Brussels VUB, 1–12 (1989)

  7. de WEGER, B.M.M.: Approximation lattices of p-adic numbers. J. Number Theory24, 70–88 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  8. de WEGER, B.M.M.: Periodicity of p-adic continued fractions. Elem. Math.43, 112–116 (1988)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Author notes

  1. Edmondo Bedocchi

    Present address: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, I-40127, Bologna, Italia

Authors and Affiliations

    Authors
    1. Edmondo Bedocchi
      View author publications

      You can also search for this author in PubMed Google Scholar

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Bedocchi, E. Sur le developpement de\(\sqrt m\) en fraction continue p-adiqueen fraction continue p-adique. Manuscripta Math 67, 187–195 (1990). https://doi.org/10.1007/BF02568429

    Download citation

    • Received:

    • Revised:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF02568429

    Search

    Navigation