Remote Access St. Petersburg Mathematical Journal

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
Published electronically: November 17, 2005
MathSciNet review: 2117450
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 11D75, 11J25

Retrieve articles in all journals with MSC (2000): 11D75, 11J25

Additional Information

A. Dubickas
Affiliation: Mathematics and Informatics Department, Vilnius University, Naugarduko 24, Vilnius 03225, Lithuania

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

American Mathematical Society