Description of spectra of quadratic Pisot units

作者：Masakova Zuzana^*; Pastircakova Katerina; Pelantova Edita

来源：Journal of Number Theory, 2015, 150: 168-190.

DOI：10.1016/j.jnt.2014.11.011

• Pisot numbers
• Spectrum
• Interval exchange

The spectrum of a real number beta > 1 is the set X-m(beta) of p(beta) where p ranges over all polynomials with coefficients restricted to A = {0,1, ..., m}. For a quadratic Pisot unit beta, 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 beta instead of beta, the gap sequence of the modified spectrum is a coding of an exchange of three intervals.

• 出版日期2015-5