Geodesic
Exact Inequalities for the Norms of Factors of Polynomials
Canadian journal of mathematics, Tome 46 (1994) no. 4, pp. 687-698

Voir la notice de l'article provenant de la source Cambridge University Press

This paper addresses a number of questions concerning the size of factors of polynomials. Let p be a monic algebraic polynomial of degree n and suppose q 1 q 2 ... q i is a monic factor of p of degree m. Then we can, in many cases, exactly determine Here ‖ . ‖ is the supremum norm either on [—1, 1] or on {|z| ≤ 1}. We do this by showing that, in the interval case, for each m and n, the n-th Chebyshev polynomial is extremal. This extends work of Gel'fond, Mahler, Granville, Boyd and others. A number of variants of this problem are also considered.
DOI : 10.4153/CJM-1994-038-8
Mots-clés : 26D05, 30C10, 41A10, polynomials, factors, Chebyshev polynomials, inequalities 
Borwein, Peter B. Exact Inequalities for the Norms of Factors of Polynomials. Canadian journal of mathematics, Tome 46 (1994) no. 4, pp. 687-698. doi: 10.4153/CJM-1994-038-8
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