Elsevier

Journal of Number Theory

Volume 150, May 2015, Pages 168-190
Journal of Number Theory

Description of spectra of quadratic Pisot units

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Abstract

The spectrum of a real number β>1 is the set Xm(β) of p(β) where p ranges over all polynomials with coefficients restricted to A={0,1,,m}. For a quadratic Pisot unit β, we determine the values of all distances between consecutive points and their corresponding frequencies, by recasting the spectra in the frame of the cut-and-project scheme. We also show that shifting the set A of digits so that it contains at least one negative element, or considering negative base −β instead of β, the gap sequence of the modified spectrum is a coding of an exchange of three intervals.

MSC

11K16
11A63

Keywords

Pisot numbers
Spectrum
Interval exchange

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