Hausdorff measure of zeros of polynomials

Fuente: arXiv
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Autori principali: Murdza, Andrew, Nguyen, Khai T., Phillips, Etienne
Natura: Preprint
Pubblicazione: 2023
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author Murdza, Andrew
Nguyen, Khai T.
Phillips, Etienne
author_facet Murdza, Andrew
Nguyen, Khai T.
Phillips, Etienne
contents 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 $p$.
format Preprint
id arxiv_https___arxiv_org_abs_2312_17462
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Hausdorff measure of zeros of polynomials
Murdza, Andrew
Nguyen, Khai T.
Phillips, Etienne
Classical Analysis and ODEs
Algebraic Geometry
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 $p$.
title Hausdorff measure of zeros of polynomials
topic Classical Analysis and ODEs
Algebraic Geometry
url https://arxiv.org/abs/2312.17462