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arXiv · 2507.15908

Distribution of the roots of Eulerian polynomials

Paul Melotti
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Abstract

We give a new proof that the empirical measures of the roots of Eulerian polynomials converge to a certain log-Cauchy distribution. To do so, we show that each moment of the roots of a related family of polynomials not only converge, but in fact become ultimately constant. These asymptotic moments are expressed in terms of Cauchy numbers of the second kind.

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Paul Melotti. 2025-11-13. Distribution of the roots of Eulerian polynomials. https://arxiv.org/abs/2507.15908

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