On a problem of Nesterenko: when is the closest root of a polynomial a real number? (Q2880337)
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scientific article; zbMATH DE number 6023786
| Language | Label | Description | Also known as |
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| English | On a problem of Nesterenko: when is the closest root of a polynomial a real number? |
scientific article; zbMATH DE number 6023786 |
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13 April 2012
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resultant of integer polynomial
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classification of roots of polynomials
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On a problem of Nesterenko: when is the closest root of a polynomial a real number? (English)
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Let \(P\) be a nonzero integer polynomial of height \(H\). It is possible to prove that, if \(w\) is large enough and if \(|P(x)|<H^{-w}\) for some complex number \(x\), then ``the'' root of \(P\) closest to \(x\) is real. The authors prove that this is true for \(w>2n-3\) if \(H\) is sufficiently large. They also bound the distance between \(x\) and ``the'' root of \(P\) closest to \(x\).
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