Abstract.
Here we provide a necessary and sufficient condition on the partial quotients of two real quadratic irrational numbers to insure that they are elements of the same quadratic number field over ℚ. Such a condition has implications to simultaneous diophantine approximation. In particular, we deduce an improvement to Dirichlet’s Theorem in this context which, as an immediate consequence, shows the Littlewood Conjecture to hold for all numbers α and β both from . Specifically, for all such pairs we have .
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
(Received 10 August 1998; in revised form 23 November 1998)
Rights and permissions
About this article
Cite this article
Burger, E. On Real Quadratic Number Fields and Simultaneous Diophantine Approximation. Mh Math 128, 201–209 (1999). https://doi.org/10.1007/s006050050058
Issue Date:
DOI: https://doi.org/10.1007/s006050050058