On the Distribution of Critical Points of a Polynomial

Sneha Dey Subramanian

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arXiv · 1207.0125

On the Distribution of Critical Points of a Polynomial

Sneha Dey Subramanian

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Abstract

This paper proves that if points $Z_1,Z_2,...$ are chosen independently and identically using some measure $μ$ from the unit circle in the complex plane, with $p_n(z) = (z-Z_1)(z-Z_2)...(z-Z_n)$, then the empirical distribution of the critical points of $p_n$ converges weakly to $μ$.

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BibTeX RIS

Sneha Dey Subramanian. 2012-10-19. On the Distribution of Critical Points of a Polynomial. https://arxiv.org/abs/1207.0125

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