Numerische Mathematik

, Volume 55, Issue 6, pp 711–733 | Cite as

Some observations on the distribution of values of continued fractions

  • L. Jacobsen
  • W. J. Thron
  • H. Waadeland


There have been many studies of the values taken on by continued fractionsK(a n /1) when its elements are all in a prescribed setE. The set of all values taken on is the limit regionV(E). It has been conjectured that the values inV(E), are taken on with varying probabilities even when the elementsa n are uniformly distributed overE. In this article, we present the first concrete evidence that this is indeed so. We consider two types of element regions: (A)E is an interval on the real axis. Our best results are for intervals [−ρ(1−ρ), ρ(1−ρ)], 0 <ρ≦1/2. (B)E is a disk in the complex plane defined byE={z:|z|≦ρ(1−ρ)}., 0<ρ≦1/2.

Subject Classifications

AMS(MOS):30B70 65D15 CR:G1.2 


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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • L. Jacobsen
    • 1
  • W. J. Thron
    • 2
  • H. Waadeland
    • 1
  1. 1.Department of Mathematics and StatisticsThe University of TrondheimDragvollNorway
  2. 2.Department of MathematicsUniversity of ColoradoBoulderUSA

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