Algebraic numbers with elements of small height

Goral H.

MATHEMATICAL LOGIC QUARTERLY, vol.65, no.1, pp.14-22, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 65 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1002/malq.201700043
  • Journal Name: MATHEMATICAL LOGIC QUARTERLY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.14-22
  • Dokuz Eylül University Affiliated: Yes

Abstract

In this paper, we study the field of algebraic numbers with a set of elements of small height treated as a predicate. We prove that such structures are not simple and have the independence property. A real algebraic integer >1 is called a Salem number if and 1/ are Galois conjugate and all other Galois conjugates of lie on the unit circle. It is not known whether 1 is a limit point of Salem numbers. We relate the simplicity of a certain pair with Lehmer's conjecture and obtain a model-theoretic characterization of Lehmer's conjecture for Salem numbers.