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A seminal result due to Wall states that if $x$ is normal to a given base $b$ , then so is $rx+s$ for any rational numbers $r,s$ with $r\neq 0$… Click to show full abstract
A seminal result due to Wall states that if $x$ is normal to a given base $b$ , then so is $rx+s$ for any rational numbers $r,s$ with $r\neq 0$ . We show that a stronger result is true for normality with respect to the continued fraction expansion. In particular, suppose $a,b,c,d\in \mathbb{Z}$ with $ad-bc\neq 0$ . Then if $x$ is continued fraction normal, so is $(ax+b)/(cx+d)$ .
Keywords:
non trivial;
preserve normality;
normality;
matrix actions;
actions preserve;
trivial matrix
Journal Title: Compositio Mathematica
Year Published: 2017
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Journal Title: Compositio Mathematica
Year Published: 2017
Link to full text (if available)
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recommendations!