Annales Academiæ Scientiarum Fennicæ

Mathematica

Volumen 45, 2020, 601-606

# SMALL DISCS CONTAINING
CONJUGATE ALGEBRAIC INTEGERS

## Artūras Dubickas

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.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4524

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