How the Roots of a Polynomial Vary with its Coefficients: A Local Quantitative Result

@inproceedings{Beauzamy1999HowTR,
  title={How the Roots of a Polynomial Vary with its Coefficients: A Local Quantitative Result},
  author={Bernard Beauzamy},
  year={1999}
}
A well-known result, due to Ostrowski, states that ifkP Qk2<", then the roots (x j )o f Pand (y j ) of Q satisfyjx j y jjCn"1=n, where n is the degree of P and Q. Though there are cases where this estimate is sharp, it can still be made more precise in general, in two ways: first by using Bombieri's norm instead of the classical l1 or l2 norms, and second by taking into account the multiplicity of each root. For instance, if x is a simple root of P, we show thatjx yj< C" instead of" 1=n . The… CONTINUE READING

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