Hawaii conjecture through the lens of Cauchy indices
Number Theory
2025-06-30 v1 Classical Analysis and ODEs
Abstract
Given a real polynomial , we study some properties of real critical points of its logarithmic derivative using the theory of Cauchy indices. As a by-product we improve the lower bound for the number these points.
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}
}