ON A PROBLEM RELATED TO NUMBER SYSTEMS

Author:

Paulius~DRUNGILAS

2010 Mathematics Subject Classification:

11R11, 11R04

Keywords:

canonical number system, expanding algebraic integer.

Abstract:

Let \alpha be an algebraic integer whose all the conjugates (including \alpha itself)  lie strictly outside the unit circle. Let \mathcal{B}=\big\{0,\pm 1,\ldots,\pm \big(|N(\alpha)|-1\big)\big\}, where N(\alpha) stands for the absolute norm of \alpha. We give an explicit proof of {\mathbb Z}[\alpha]=\mathcal{B}[\alpha] for quadratic integer \alpha.

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Drun-2012

Vol. 7 (15), 2011