The aim of this book is to give a survey of results in the theory of algebraic numbers
achieved in the first half of the twentieth century and may be viewed as a companion to my …

The diameter of a totally real algebraic integer α of degree d with conjugates α 1< α 2<...< α
d is diam (α)= α d− α 1. For all positive integers k and n, diam (2 cos (2kπ/n)) is less than 4 …

Let f (x)∈ Z [x] be a totally real polynomial with roots α 1≤...≤ α d. The span of f (x) is
defined to be α d− α 1. Monic irreducible f (x) of span less than 4 are special. In this paper …

We study two infinite sequences of polynomials related to Jordan blocks that have various
interesting properties. We show that they are orthogonal polynomials whose sequences of …

Dans ce travail, nous proposons une nouvelle méthode destinée à trouver des polynômes
unitaires irréductibles à racines réelles, à coefficients entiers, et dont le diamètre soit …

Abstract In 1993 Estes and Guralnick conjectured that any totally real separable monic
polynomial with rational integer coefficients will occur as the minimal polynomial of some …

A monic, irreducible polynomial in one variable having integer coefficients and all real roots
deserves particular interest if its roots lie in an interval of length 4 whose end-points are not …

This thesis has been motivated largely by Lehmer's problem [20], which was stated in 1933
and it is still a problem that mathematicians have not completely solved. The Mersenne …

Consider an algebraic number a. By definition, it is the zero in some field of an irreducible
polynomial Pa with integer coefficients. The complete set of zeros of such a polynomial …

A totally-real polynomial in $\mathbb {Z}[x] $ with zeros $\alpha _1\leqslant\alpha
_2\leqslant\dots\leqslant\alpha _d $ has span $\alpha _d-\alpha _1 $. Building on the …