Title: Each univariate complex polynomial has a ‘big’ factor
Abstract: We consider the following problem: Let P be a monic polynomial of degree n with complex coefficients. What can be the maximum ‘size’ of a monic divisor Q of P ? Here the size of a polynomial R is the maximum || R || of the moduli of its values on the unit circle. In 1991, B. Beauzamy proved that there exists a divisor Q with ||Q|| ≧ e ∈n−1 , ∈ = 0.0019, when all the roots of P belong to the unit circle. Using a very recent result of D. Boyd, we obtain a general result which, in the same case, gives ||Q||≧β n ; here β = 1.38135 … is optimal.
Publication Year: 1994
Publication Date: 1994-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 1
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