Annales Academiæ Scientiarum Fennicæ
Volumen 45, 2020, 601-606
Vilnius University, Faculty of Mathematics and Informatics,
Institute of Mathematics
Naugarduko 24, LT-03225 Vilnius, Lithuania; arturas.dubickas 'at' mif.vu.lt
Abstract. In this note we show that, for any ξ ∈ R, there is an infinite set of positive integers S such that, for each d ∈ S, the open disc with center at ξ and radius 1 + (log log d)2/(2 log d) contains a full set of conjugates of an algebraic integer of degree d. A slightly better bound on the radius is established when ξ ∈ Q \ Z.
2010 Mathematics Subject Classification: Primary 11R04, 11R09.
Key words: Conjugate algebraic integers, disc with real center, diameter of algebraic integer, Rouché's theorem.
Reference to this article: A. Dubickas: Small discs containing conjugate algebraic integers. Ann. Acad. Sci. Fenn. Math. 45 (2020), 601-606.
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