Chebyshev coordinates and Salem numbers

2018/12/31 by Stefano Capparelli, Capparelli, Stefano, Alberto Del Fra +1
Mathematics · Physics and Astronomy · #11R09 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1812.11869

openalex publication_date 2018/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By expressing polynomials in the basis of Chebyshev polynomials, certain families of hyperbolic polynomials appear naturally. Some of these families have all their roots in the interval [-2,2]. In many cases the span of the family of polynomials thus found is greater than 4, and we show that they are the minimal polynomials of Salem numbers, possibly multiplied by some cyclotomic polynomials. In addition, we show how to compute the limit of the largest and smallest roots.

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