Discrete spectra and Pisot numbers

JOURNAL OF NUMBER THEORY

卷:133

Article

Akiyama, Shigeki¹  Komornik, Vilmos² 

[1] Univ Tsukuba, Inst Math, Tsukuba, Ibaraki 3500006, Japan

[2] Univ Strasbourg, Dept Math, F-67084 Strasbourg, France

关键词: Pisot number;    Radix expansion;    Spectrum;   

DOI  :  10.1016/j.jnt.2012.07.015

来源: Elsevier

【 摘 要 】

By the m-spectrum of a real number q > 1 we mean the set Y-m(q) of values p(q) where p runs over the height m polynomials with integer coefficients. These sets have been extensively investigated during the last fifty years because of their intimate connections with infinite Bernoulli convolutions, spectral properties of substitutive point sets and expansions in noninteger bases. We prove that Y-m(q) has an accumulation point if and only if q < m land q is not a Pisot number. Consequently a number of related results on the distribution of points of this form are improved. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free