Hawaii conjecture through the lens of Cauchy indices

2025/06/27 by Gnatyuk, Dmitry, Tyaglov, Mikhail
#26C10 #30C10 #30C15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2506.22330

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.

Citations

• On the number of real critical points of logarithmic derivatives and the Hawaii conjecture
• Lectures on the Routh-Hurwitz problem

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