On asymptotics of the uniform norm of polynomials with zeros at the roots of unity (Q705780)
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scientific article; zbMATH DE number 2133967
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On asymptotics of the uniform norm of polynomials with zeros at the roots of unity |
scientific article; zbMATH DE number 2133967 |
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On asymptotics of the uniform norm of polynomials with zeros at the roots of unity (English)
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14 February 2005
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The motivation of this paper is a problem of Erdős about the estimation of the numbers \[ A_N = \max_{| z| =1} \bigl| (z-z_1) \cdots (z-z_N)\bigr| , \] where \(z_1\), \dots, \(z_N\) are complex numbers of modulus \(1\), and \(N\) tends to infinity. Here the authors consider the case where the \(z_j\)'s are roots of unity. They obtain sharp estimates of \(A_N\) in this case. Their result implies that \(\log A_N\) grows like \(\sqrt N\). The proof involves a very precise study.
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norm of polynomials
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roots of unity
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