Conjugate algebraic numbers close to a symmetric set

Dubickas, A.

doi:10.1090/S1061-0022-05-00887-3

Conjugate algebraic numbers close to a symmetric set
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by A. Dubickas
Translated by: A. Plotkin

St. Petersburg Math. J. 16 (2005), 1013-1016

DOI: https://doi.org/10.1090/S1061-0022-05-00887-3

Published electronically: November 17, 2005

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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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