Eprints of Rényi Institute

Nonstandard analysis: Sparse Polynomials

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



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)
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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