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arXiv · 1106.4219

Number systems and the Chinese Remainder Theorem

Christiaan E. van de Woestijne
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Abstract

A well-known generalisation of positional numeration systems is the case where the base is the residue class of $x$ modulo a given polynomial $f(x)$ with coefficients in (for example) the integers, and where we try to construct finite expansions for all residue classes modulo $f(x)$, using a suitably chosen digit set. We give precise conditions under which direct or fibred products of two such polynomial number systems are again of the same form. The main tool is a general form of the Chinese Remainder Theorem. We give applications to simultaneous number systems in the integers.

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Christiaan E. van de Woestijne. 2011-06-21. Number systems and the Chinese Remainder Theorem. https://arxiv.org/abs/1106.4219

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