English

Hawaii conjecture through the lens of Cauchy indices

Number Theory 2025-06-30 v1 Classical Analysis and ODEs

Abstract

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

Keywords

Cite

@article{arxiv.2506.22330,
  title  = {Hawaii conjecture through the lens of Cauchy indices},
  author = {Dmitry Gnatyuk and Mikhail Tyaglov},
  journal= {arXiv preprint arXiv:2506.22330},
  year   = {2025}
}