Archiv der Mathematik

, Volume 44, Issue 4, pp 340–347

Euclidean real quadratic number fields

  • David H. Johnson
  • Clifford S. Queen
  • Alicia N. Sevilla
Article
  • 76 Downloads

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E. S. Barnes andH. P. F. Swinnerton-Dyer, The inhomogeneous minima of binary quadratic forms I. Acta Math.87, 259–323 (1952).Google Scholar
  2. [2]
    Erick Berg, Über die Existenz eines Euklidischen Algorithmus in quadratischen Zahlkörpern. Kungl. Fysiografiska Sallskapets Lund Forhandlingar (5)5, 521–526 (1935).Google Scholar
  3. [3]
    Paul Erdös andChao Ko, Note on the Euclidean Algorithm. J. London Math. Soc.13, 3–8 (1938).Google Scholar
  4. [4]
    H. Davenport, Indefinite binary quadratic forms and Euclid's algorithm in real quadratic fields. Proc. London Math. Soc. (2)53, 75–82 (1951).Google Scholar
  5. [5]
    H. Heilbronn, On Euclid's Algorithm in Real Quadratic Fields. Proc. Cambridge Phil. Soc.34, 521–526 (1938).Google Scholar
  6. [6]
    H. W.Lenstra, Lectures on Euclidean Rings. Bielefeld 1974.Google Scholar
  7. [7]
    H. W. Lenstra, Euclidean Ideal Classes. Astirisque61, 121–131 (1979).Google Scholar
  8. [8]
    C. Queen, Arithmetic Euclidean rings. Acta Arithm.26, 105–113 (1974).Google Scholar
  9. [9]
    C. Queen, Some arithmetic properties of subrings of function fields over finite fields. Arch. Math.26, 51–56 (1975).Google Scholar
  10. [10]
    P. Samuel, About Euclidean Rings. J. Algebra19, 282–301 (1971).Google Scholar
  11. [11]
    P.Weinberger, On Euclidean rings of algebraic integers. Amer. Math. Soc. Proc. Symp. Analytic Number Theory24 (1973).Google Scholar

Copyright information

© Birkhäuser Verlag 1985

Authors and Affiliations

  • David H. Johnson
    • 1
  • Clifford S. Queen
    • 1
  • Alicia N. Sevilla
    • 1
  1. 1.Department of MathematicsLehigh UniversityBethlehemUSA

Personalised recommendations