Csirmaz, László (2006) *Nonstandard analysis: Sparse Polynomials.* In: Habilitation, University of Debrecen.

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## Abstract

We prove the theorem of Kakeya and Montel using nonstandard methods: there exists a number $\rho$ depending only on $n$ and $k$ such that if the polynomial $p(z)$ of degree $n$ has $k$ roots in the unit circle, then the derivative of $p(z)$ has at least $k-1$ roots in the circle of radius $\rho$. The method yields several generalizations as well.

Item Type: | Presentation (Presentation) |
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Keywords and phrases: | nonstandard analysis, roots of polynomials, sparse polynomials |

Subjects: | 30A99 General properties - other 26E35 Nonstandard analysis |

Divisions: | Research Groups > Theoretical cryptography |

Last Modified: | 18 Jul 2009 20:15 |

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