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arXiv · 2312.17462

Hausdorff measure of zeros of polynomials

Andrew Murdza·Khai T. Nguyen·Etienne Phillips
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Abstract

The paper provides an elementary proof establishing a sharp universal bound on the $(d-1)$-Hausdorff measure of the zeros of any nontrivial multivariable polynomial $p:\mathbb{R}^d\to\mathbb{R}$ within a $d$-dimensional cube of size $r$. This bound depends solely on the parameter $r$, the dimension $d$, and the degrees of $p$.

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BibTeXRIS

Andrew Murdza, Khai T. Nguyen, Etienne Phillips. 2023-12-29. Hausdorff measure of zeros of polynomials. https://arxiv.org/abs/2312.17462

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