Asympotic bounds for Bombieri's inequality on products of homogeneous polynomials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929259456495616 |
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| author | Aldaz, J. M. Render, H. |
| author_facet | Aldaz, J. M. Render, H. |
| contents | Let $P$ be a fixed homogeneous polynomial. We present a sharp condition on $P$ guaranteeing the existence of asymptotically larger bounds in Bombieri's inequality, so for every homogeneous polynomial $q_m$ of degree $m$ we have \begin{equation*} \left\Vert P q_{m}\right\Vert _{a}\geq C_{P} m^{l\left( P\right) /2}\left\Vert q_{m}\right\Vert _{a}, \end{equation*} where $\| \cdot \| _{a}$ denotes the apolar norm. Explicit estimates for $C_P > 0$ and $l(P) > 0$ are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asympotic bounds for Bombieri's inequality on products of homogeneous polynomials Aldaz, J. M. Render, H. Analysis of PDEs Let $P$ be a fixed homogeneous polynomial. We present a sharp condition on $P$ guaranteeing the existence of asymptotically larger bounds in Bombieri's inequality, so for every homogeneous polynomial $q_m$ of degree $m$ we have \begin{equation*} \left\Vert P q_{m}\right\Vert _{a}\geq C_{P} m^{l\left( P\right) /2}\left\Vert q_{m}\right\Vert _{a}, \end{equation*} where $\| \cdot \| _{a}$ denotes the apolar norm. Explicit estimates for $C_P > 0$ and $l(P) > 0$ are given. |
| title | Asympotic bounds for Bombieri's inequality on products of homogeneous polynomials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.19153 |