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Some computations on the spectra of Pisot and Salem numbers |
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| Authors: | Peter Borwein Kevin G. Hare. |
| Affiliation: | Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 ; Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 |
| Abstract: | Properties of Pisot numbers have long been of interest. One line of questioning, initiated by Erdos, Joó and Komornik in 1990, is the determination of  for Pisot numbers  , where  Although the quantity  is known for some Pisot numbers  , there has been no general method for computing  . This paper gives such an algorithm. With this algorithm, some properties of  and its generalizations are investigated. A related question concerns the analogy of |
| Keywords: | Pisot numbers LLL spectrum beta numbers |
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, denoted 
, where the coefficients are restricted to 
; in particular, for which non-Pisot numbers is 
nonzero? This paper finds an infinite class of Salem numbers where 
.