A bilinear estimate in $\mathbb{F}_p$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913197545488384 |
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| author | Kavrut, Necef Wu, Shukun |
| author_facet | Kavrut, Necef Wu, Shukun |
| contents | We improve an $L^2\times L^2\to L^2$ estimate for a certain bilinear operator in the finite field of size $p$, where $p$ is a prime sufficiently large. Our method carefully picks the variables to apply the Cauchy-Schwarz inequality. As a corollary, we show that there exists a quadratic progression $x,x+y,x+y^2$ for nonzero $y$ inside any subset of $\mathbb{F}_p$ of density $\gtrsim p^{-1/8}$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A bilinear estimate in $\mathbb{F}_p$ Kavrut, Necef Wu, Shukun Classical Analysis and ODEs Number Theory We improve an $L^2\times L^2\to L^2$ estimate for a certain bilinear operator in the finite field of size $p$, where $p$ is a prime sufficiently large. Our method carefully picks the variables to apply the Cauchy-Schwarz inequality. As a corollary, we show that there exists a quadratic progression $x,x+y,x+y^2$ for nonzero $y$ inside any subset of $\mathbb{F}_p$ of density $\gtrsim p^{-1/8}$ |
| title | A bilinear estimate in $\mathbb{F}_p$ |
| topic | Classical Analysis and ODEs Number Theory |
| url | https://arxiv.org/abs/2401.07925 |