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Abstract <p>Given a real polynomial <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p\)</EquationSource> <!--LobJMat2561095Gnatyuk-m1--> </InlineEquation>, we study some properties of real critical points of its logarithmic derivative <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(Q[p]=(p^{\prime}/p)^{\prime}\)</EquationSource> <!--LobJMat2561095Gnatyuk-m2--> </InlineEquation> using the theory of Cauchy indices. As a by-product, we improve the lower bound for the number of these points.</p>

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Hawaii Conjecture Through the Lens of Cauchy Indices

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • D. Gnatuyk,
  • M. Tyaglov

摘要

Abstract

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