Number systems and the Chinese Remainder Theorem

2011/06/21 by Christiaan E. van de Woestijne, van de Woestijne, Christiaan E.
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #History and Theory of Mathematics #math.AC #math.NT #msc:11A63 #msc:13F10 #msc:13P15

paper · pdf · doi:10.48550/arxiv.1106.4219

17 pages

arxiv created 2011/06/21 · arxiv updated 2011/06/22

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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