Some computations on the spectra of Pisot and Salem numbers期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Some computations on the spectra of Pisot and Salem numbers

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 $begin{displaymath}l(q) = inf(vert yvert: y = epsilon_0 + epsilon_1 q^1 + cdots + epsilon_n q^n, epsilon_i in {pm 1, 0}, y neq 0).end{displaymath}$ 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 , 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 .

Keywords:	Pisot numbers LLL spectrum beta numbers

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