Algebraic numbers with elements of small height | Zendy

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Algebraic numbers with elements of small height

Author(s) -

Göral Haydar

Publication year - 2019

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.201700043

Subject(s) - mathematics , conjecture , algebraic extension , algebraic number , simple (philosophy) , discrete mathematics , combinatorics , pure mathematics , mathematical analysis , differential algebraic equation , ordinary differential equation , philosophy , epistemology , differential equation

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 α > 1 is called a Salem number if α and 1 / α are Galois conjugate and all other Galois conjugates of α 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.

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