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arXiv · 1105.4321

Geometrical aspects of expansions in complex bases

Anna Chiara Lai
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Abstract

We study the set of the representable numbers in base $q=pe^{i\frac{2π}{n}}$ with $ρ>1$ 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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Anna Chiara Lai. 2011-05-22. Geometrical aspects of expansions in complex bases. https://arxiv.org/abs/1105.4321

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