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Products of polynomials and a priori estimates for coefficients in polynomial decompositions: A sharp result. (English) Zbl 0757.30002

The author introduces a weighted, submultiplicative \(\ell_ 2\) norm \([\cdot]_ 2\) on the space of polynomials in one variable. He shows that \([Q]_ 2[R]_ 2/[QR]_ 2\) is bounded by \(\sqrt{(m+n)!/m!n!}\) for any polynomials \(Q\) and \(R\) in one variable of degrees \(m\) and \(n\) respectively. Using this result, he gives a priori estimate for the size of the coefficients in any factor of a polynomial with integer coefficients.
Reviewer: Y.Avci (İstanbul)

MSC:

30C10 Polynomials and rational functions of one complex variable
12E05 Polynomials in general fields (irreducibility, etc.)
26D05 Inequalities for trigonometric functions and polynomials
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References:

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