Hausdorff measure of zeros of polynomials
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916225841364992 |
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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 |