Constructions of Pisot and Salem numbers with flat palindromes
type: Item
instance of: scholarly article
title: Constructions of Pisot and Salem numbers with flat palindromes
zbMATH Open document ID: 1178.11069
author: Shigeki Akiyama
author: Do Yong Kwon
published in: Monatshefte für Mathematik
publication date: 2009-06-22T00:00:00Z
review text: Using interlacing and the argument principle, the paper proves some conditions under which some special families of polynomials define Salem numbers or Pisot numbers. Their theorems are concerned with monic reciprocal polynomials \(f(x) = x^n - \sum_{k=1}^{n-1} a_k x^k + 1\) with integer coefficients for which the coefficient sequence \(\{a_k\}_{k=1}^{n-1}\) is in some sense a small perturbation of a constant sequence, and the related polynomials \(g(x) = (f(x)-1)/x\). For example, they show that if \(b \geq [(n-1)/2]\) is an integer and if \(a_k = a_{n-k}\) and \(a_k \in [b,b-1]\) for \(k = 1,\dots,n-1\), then \(g(x)\) defines a Pisot number.
reviewed by: David W. Boyd
Mathematics Subject Classification ID: 11R06
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 5566997
zbMATH Keywords: Pisot number
zbMATH Keywords: Salem number
MaRDI profile type: Publication
full work available at URL: s00605-008-0011-0
OpenAlex ID: W2097197200
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DOI: 10.1007/S00605-008-0011-0
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description: scientific article; zbMATH DE number 5566997