Constructions of Pisot and Salem numbers with flat palindromes
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.
scientific article; zbMATH DE number 5566997
scientific article