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arXiv · 1307.5731

Means of algebraic numbers in the unit disk

Igor E. Pritsker
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Abstract

Schur studied limits of the arithmetic means $s_n$ of zeros for polynomials of degree $n$ with integer coefficients and simple zeros in the closed unit disk. If the leading coefficients are bounded, Schur proved that $\limsup_{n\to\infty} |s_n| \le 1-\sqrt{e}/2.$ We show that $s_n \to 0$, and estimate the rate of convergence by generalizing the Erdős-Turán theorem on the distribution of zeros.

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Igor E. Pritsker. 2013-07-22. Means of algebraic numbers in the unit disk. https://arxiv.org/abs/1307.5731

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