Algebraic numbers with elements of small height

Goral H.

MATHEMATICAL LOGIC QUARTERLY, cilt.65, sa.1, ss.14-22, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 65 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1002/malq.201700043
  • Dergi Adı: MATHEMATICAL LOGIC QUARTERLY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.14-22
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.