On the zeros of an algebraic polynomial and its consecutive derivatives (Q2762972)
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scientific article; zbMATH DE number 1689821
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the zeros of an algebraic polynomial and its consecutive derivatives |
scientific article; zbMATH DE number 1689821 |
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16 January 2002
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zeros of polynomials
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consecutive derivative
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On the zeros of an algebraic polynomial and its consecutive derivatives (English)
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This paper generalizes Sendov's conjecture from 1958 which states that if all the zeros of a monic algebraic polynomial lie in the unit disk then every disk with center a zero of this polynomial and radius one contains at least one zero of the derivative. The generalized conjecture says that under the same conditions one can define a little bit bigger disk that contains at least one zero of any derivative of order less than the order of the polynomial. This conjecture is proved for particular cases according to the order of the polynomial and the derivatives.
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