The Möbius transformation of continued fractions with bounded upper and lower partial quotients

Abstract

Let $h$: $x\mapsto \frac{ax+b}{cx+d}$ be the nondegenerate Möbius transformation with integer entries. We get a bound of the continued fraction of $h(x)$ by the upper and lower bound of continued fraction of $x$, which extends a result of Stambul \cite{S2}.

Cited by in corpus (1)

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