Salem numbers of trace -2, and a conjecture of Estes and Guralnick. / McKee, James; Yatsyna, Pavlo.

In: Journal of Number Theory, Vol. 160, 03.2016, p. 409–417.

Research output: Contribution to journalArticle

Published

Documents

Links

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 symmetric matrix with rational integer entries. They proved this to be true for all such polynomials that have degree at most 4. In this paper, we show that for every d>=6 there is a polynomial of degree d that is a counterexample to this conjecture. The only case still in doubt is degree 5. One of the ingredients in the proof is to show that there are Salem numbers of degree 2d and trace -2 for every d>=12.
Original languageEnglish
Pages (from-to)409–417
Number of pages9
JournalJournal of Number Theory
Volume160
Early online date2 Nov 2015
DOIs
Publication statusPublished - Mar 2016
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

ID: 25550724