Vol. 9, No. 4, 2020

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Algebraic integers close to the unit circle

Artūras Dubickas

Vol. 9 (2020), No. 4, 361–370
Abstract

We show that for each d 3 there is a monic integer polynomial P of degree d which is irreducible over  and has two complex conjugate roots as close to the unit circle as is allowed by the Liouville-type inequality.

Keywords
irreducible polynomial, roots close to 1, Mahler measure, resultant
Mathematical Subject Classification 2010
Primary: 11C08
Secondary: 12D10
Milestones
Received: 7 October 2019
Revised: 13 January 2020
Accepted: 27 January 2020
Published: 5 November 2020
Authors
Artūras Dubickas
Institute of Mathematics
Faculty of Mathematics and Informatics
Vilnius University
Vilnius
Lithuania