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arXiv · 1712.04225

Piecewise interlacing zeros of polynomials

David G. L. Wang·Jiarui Zhang
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Abstract

We introduce the concept of piecewise interlacing zeros for studying the relation of root distribution of two polynomials. The concept is pregnant with an idea of confirming the real-rootedness of polynomials in a sequence. Roughly speaking, one constructs a collection of disjoint intervals such that one may show by induction that consecutive polynomials have interlacing zeros over each of the intervals. We confirm the real-rootedness of some polynomials satisfying a recurrence with linear polynomial coefficients. This extends Gross et al.'s work where one of the polynomial coefficients is a constant.

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David G. L. Wang, Jiarui Zhang. 2018-05-07. Piecewise interlacing zeros of polynomials. https://arxiv.org/abs/1712.04225

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