Nonstandard analysis: Sparse Polynomials

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) nonstandard analysis, roots of polynomials, sparse polynomials 30A99 General properties - other26E35 Nonstandard analysis Research Groups > Theoretical cryptography 18 Jul 2009 20:15

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