On a theorem of Mattila in the p-adic setting Article Swipe

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Boqing Xue , Thang Pham , Le Quoc Hung , Le Q. Ham , Nguyen D. Phuong ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2502.05818

Let $A, B$ be subsets of $(\mathbb{Z}/p^r\mathbb{Z})^2$. In this note, we provide conditions on the densities of $A$ and $B$ such that $|gA-B|\gg p^{2r}$ for a positive proportion of $g\in SO_2(\mathbb{Z}/p^r\mathbb{Z})$. The conditions are sharp up to constant factors in the unbalanced case, and the proof makes use of tools from discrete Fourier analysis and results in restriction/extension theory.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2502.05818
PDF: https://arxiv.org/pdf/2502.05818
OA Status: green
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DOI: https://doi.org/10.48550/arxiv.2502.05818

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Title: On a theorem of Mattila in the p-adic setting

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-02-09

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Authors: Boqing Xue, Thang Pham, Le Quoc Hung, Le Q. Ham, Nguyen D. Phuong

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Landing page: https://arxiv.org/abs/2502.05818

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PDF URL: https://arxiv.org/pdf/2502.05818

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Open access: Yes

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OA URL: https://arxiv.org/pdf/2502.05818

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Concepts: Psychology, Medicine

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