High-low analysis and small cap decoupling over non-Archimedean local fields
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909803224236032 |
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| author | Johnsrude, Ben |
| author_facet | Johnsrude, Ben |
| contents | We prove a small cap decoupling theorem for the parabola over a general non-Archimedean local field for which $2\neq 0$. We obtain polylogarithmic dependence on the scale parameter $R$ and polynomial dependence in the residue prime, except for the prime 2 for which the polynomial depends on degree. Our constants are fully explicit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09163 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-low analysis and small cap decoupling over non-Archimedean local fields Johnsrude, Ben Classical Analysis and ODEs 43A25 (Primary), 28A80 (Secondary) We prove a small cap decoupling theorem for the parabola over a general non-Archimedean local field for which $2\neq 0$. We obtain polylogarithmic dependence on the scale parameter $R$ and polynomial dependence in the residue prime, except for the prime 2 for which the polynomial depends on degree. Our constants are fully explicit. |
| title | High-low analysis and small cap decoupling over non-Archimedean local fields |
| topic | Classical Analysis and ODEs 43A25 (Primary), 28A80 (Secondary) |
| url | https://arxiv.org/abs/2409.09163 |