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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Conjugate algebraic numbers close to a symmetric set


Author: A. Dubickas
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 16 (2004), nomer 6.
Journal: St. Petersburg Math. J. 16 (2005), 1013-1016
MSC (2000): Primary 11D75, 11J25
DOI: https://doi.org/10.1090/S1061-0022-05-00887-3
Published electronically: November 17, 2005
MathSciNet review: 2117450
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Abstract: A new proof is presented for the Motzkin theorem saying that if a set consists of $ d-1$ complex points and is symmetric relative to the real axis, then there exists a monic, irreducible, and integral polynomial of degree $ d$ whose roots are as close to each of these $ d-1$ points as we wish. Unlike the earlier proofs, the new proof is efficient, i.e., it gives both an explicit construction of the polynomial in question and the location of its $ d$th root.


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Additional Information

A. Dubickas
Affiliation: Mathematics and Informatics Department, Vilnius University, Naugarduko 24, Vilnius 03225, Lithuania
Email: arturas.dubickas@maf.vu.lt

DOI: https://doi.org/10.1090/S1061-0022-05-00887-3
Keywords: Integral polynomial, Eisenstein criterion, Salem numbers
Received by editor(s): November 22, 2003
Published electronically: November 17, 2005
Additional Notes: The work was supported in part by the Lithuanian Foundation for Research and Science
Article copyright: © Copyright 2005 American Mathematical Society