Geometrical aspects of expansions in complex bases

Details Geometrical aspects of expansions in complex bases Geometrical aspects of expansions in complex bases

2011-05-22

arxiv.org/abs/1105.4321v1

Mathematics

Number Theory

23 pages, 5 figures

Scientific paper

We study the set of the representable numbers in base $q=pe^{i\frac{2\pi}{n}}$ with $\rho>1$ and $n\in \mathbb N$ and with digits in a arbitrary finite real alphabet $A$. We give a geometrical description of the convex hull of the representable numbers in base $q$ and alphabet $A$ and an explicit characterization of its extremal points. A characterizing condition for the convexity of the set of representable numbers is also shown.

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