Results in Mathematics

, Volume 15, Issue 3–4, pp 324–334 | Cite as

P-Adic and Non-Archimedean Product Representations

  • Arnold Knopfmacher
  • John Knopfmacher
Article
  • 4 Downloads

Abstract

Two algorithms are introduced and shown to lead to a unique product representation for a given p-adic integer A with leading coefficient 1, as a product of terms \(1+{1\over a_n}\) where the a n are certain rational numbers. The degree of approximation by the N-th partial product of such terms is investigated, and in some explicit cases the products corresponding to particular types of p-adic integers are characterized. In addition, we consider similar representations for elements of arbitrary complete non-archimedean fields with discrete valuations.

AMS (1980/85) Classification Numbers

11J61 11K41 

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Copyright information

© Birkhäuser Verlag, Basel 1989

Authors and Affiliations

  • Arnold Knopfmacher
    • 1
  • John Knopfmacher
    • 2
  1. 1.Department of Computational & Applied MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa
  2. 2.Department of MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa

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