On the Lebesgue measure of sum-level sets for continued fractions

Details On the Lebesgue measure of sum-level sets for continued fractions On the Lebesgue measure of sum-level sets for continued fractions

2009-01-13

arxiv.org/abs/0901.1787v2

Mathematics

Dynamical Systems

1 figure

Scientific paper

In this paper we give a detailed measure theoretical analysis of what we call sum-level sets for regular continued fraction expansions. The first main result is to settle a recent conjecture of Fiala and Kleban, which asserts that the Lebesgue measure of these level sets decays to zero, for the level tending to infinity. The second and third main result then give precise asymptotic estimates for this decay. The proofs of these results are based on recent progress in infinite ergodic theory, and in particular, they give non-trivial applications of this theory to number theory. The paper closes with a discussion of the thermodynamical significance of the obtained results, and with some applications of these to metrical Diophantine analysis.

Affiliated with

Also associated with

No associations

Rating

On the Lebesgue measure of sum-level sets for continued fractions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Lebesgue measure of sum-level sets for continued fractions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Lebesgue measure of sum-level sets for continued fractions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-72103