On the Szüsz's Solution to Gauss' Problem
Lascu, Dan · Coltescu, Ion
الأصل · EN
The present paper deals with Gauss' problem on continued fractions. We present a new proof of a theorem which Szüsz applied in order to solve this problem. To be noted, that we obtain the value 0.7594... for q, which has been optimized by Szüsz in his 1961 paper "Über 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 τ under γ, where τ is the continued fraction transformation, and γ is the Gauss' measure.
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