Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593594 | Journal of Number Theory | 2015 | 23 Pages |
Abstract
The spectrum of a real number β>1β>1 is the set Xm(β)Xm(β) of p(β)p(β) where p ranges over all polynomials with coefficients restricted to A={0,1,…,m}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 AA 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Zuzana Masáková, Kateřina Pastirčáková, Edita Pelantová,