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Conjugate algebraic numbers close to a symmetric set
Author(s):
A.
Dubickas
Translated by:
A. Plotkin
Original publication:
Algebra i Analiz,
tom 16
(2004),
vypusk 6.
Journal:
St. Petersburg Math. J.
16
(2005),
1013-1016.
MSC (2000):
Primary 11D75, 11J25
Posted:
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  complex points and is symmetric relative to the real axis, then there exists a monic, irreducible, and integral polynomial of degree  whose roots are as close to each of these  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  th root.
References:
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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:
10.1090/S1061-0022-05-00887-3
PII:
S 1061-0022(05)00887-3
Keywords:
Integral polynomial,
Eisenstein criterion,
Salem numbers
Received by editor(s):
22/NOV/2003
Posted:
November 17, 2005
Additional Notes:
The work was supported in part by the Lithuanian Foundation for Research and Science
Copyright of article:
Copyright
2005,
American Mathematical Society
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