Hawaii conjecture through the lens of Cauchy indices

Dmitry Gnatyuk; Mikhail Tyaglov

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arXiv · 2506.22330

Hawaii conjecture through the lens of Cauchy indices

Dmitry Gnatyuk·Mikhail Tyaglov

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Abstract

Given a real polynomial $p$, we study some properties of real critical points of its logarithmic derivative $Q[p]=(p'/p)'$ using the theory of Cauchy indices. As a by-product we improve the lower bound for the number these points.

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Dmitry Gnatyuk, Mikhail Tyaglov. 2025-06-27. Hawaii conjecture through the lens of Cauchy indices. https://arxiv.org/abs/2506.22330

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