Volume 2,
Issue 1, 2001
Article
7
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INEQUALITIES
ON POLYNOMIAL HEIGHTS
LAURENTIU
PANAITOPOL AND DORU STEFANESCU
UNIVERSITY
OF BUCHAREST
70109 BUCHAREST 1
ROMANIA
E-Mail: pan@al.math.unibuc.ro
UNIVERSITY
OF BUCHAREST
PO BOX 39-D5
BUCHAREST
39
ROMANIA
E-Mail: stef@irma.u-strasbg.fr
Received 21 June, 2000; accepted 26 October 2000.
Communicated by: H. Gauchman
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ABSTRACT.
We give explicit bounds for the absolute values of the coefficients of the
divisors of a complex polynomial. They are expressed in function of the
coefficients and of upper and lower bounds for the roots. These bounds are
compared with other estimates, in particular with the inequality of Beauzamy
[B. Beauzamy, Products of polynomials and a priori estimates for
coefficients in polynomial decompositions: A sharp result, J.
Symbolic Computation, 13, 463 - 472 (1992)]. Through examples it is proved
that for some cases our evaluations give better upper limits.
Key words:
Inequalities,
Polynomials
2000 Mathematics Subject
Classification:
12D05, 12D10,
12E05, 26C05
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