Discrete spectra and Pisot numbers

2011/03/23 by Shigeki Akiyama, Akiyama, Shigeki, Vilmos Komornik +1
Computer Science · Engineering · Mathematics · #11A63 #11K16 #52C23 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT #msc:11A63 #msc:11K16 #msc:52C23 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1103.4508

arxiv created 2011/03/23 · openalex publication_date 2011/03/23 · arxiv updated 2011/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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