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

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Boqing Xue , Thang Pham , Quang-Hung Le , Quang Vinh Tin Le , Nguyen Duc Phuong ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.4153/s0008439525100866

Let $A\ \mathrm{and}\ B$ 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: article
Language: en
Landing Page: https://doi.org/10.4153/s0008439525100866
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DOI: https://doi.org/10.4153/s0008439525100866

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

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Publication year: 2025

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Publication date: 2025-07-14

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Authors: Boqing Xue, Thang Pham, Quang-Hung Le, Quang Vinh Tin Le, Nguyen Duc Phuong

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Landing page: https://doi.org/10.4153/s0008439525100866

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