Volume 2,  Issue 1, 2001

Article 7

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


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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