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arXiv · 2406.19473

Restricted projections and Fourier decoupling in $\mathbb{Q}_p^n$

Ben Johnsrude·Zuo Lin
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Abstract

We prove a restricted projection theorem for Borel subsets of $\mathbb{Q}_p^n$ in the regime $p>n$. This generalizes results of Gan-Guo-Wang in the real setting. Our result is effective in the sense that explicit constants are obtained for various covering numbers. Along the way, we prove a fully explicit Fourier decoupling theorem for the moment curve in $p$-adic Cartesian space.

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Ben Johnsrude, Zuo Lin. 2024-06-27. Restricted projections and Fourier decoupling in $\mathbb{Q}_p^n$. https://arxiv.org/abs/2406.19473

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