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Means of algebraic numbers in the unit disk
Schur studied limits of the arithmetic means sn 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 lim supn→∞ |sn| ≤ 1− √ e/2. We show that sn → 0, and estimate the rate of convergence by generalizing the Erdős-Turán theorem on the distribution of zeros. To cite this article: I. E. P...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1918
ISSN: 0386-2194
DOI: 10.3792/pia/1195582221