On the Szüsz's Solution to Gauss' Problem

Details On the Szüsz's Solution to Gauss' Problem On the Szüsz's Solution to Gauss' Problem

2010-10-21

arxiv.org/abs/1010.4432v1

Math.Sci.Res.J., 2008, vol.12(1), pp. 1-6

Mathematics

Number Theory

Scientific paper

The present paper deals with Gauss' problem on continued fractions. We present a new proof of a theorem which Sz\"usz applied in order to solve this problem. To be noted, that we obtain the value $0.7594...$ for $q$, which has been optimized by Sz\"usz in his 1961 paper "\"Uber einen Kusminschen Satz", where the value 0.485 is obtained for $q$. In our proof, we make use of an important property of the Perron-Frobenius operator of $\tau$ under $\gamma$, where $\tau$ is the continued fraction transformation, and $\gamma$ is the Gauss' measure.

Affiliated with

Also associated with

No associations

Rating

On the Szüsz's Solution to Gauss' Problem 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 Szüsz's Solution to Gauss' Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Szüsz's Solution to Gauss' Problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-423339