On a theorem of Mattila in the finite p-adic setting
Abstract 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.
Authors
- Thang Pham (ORCID: https://orcid.org/0000-0001-7600-7450)
- Boqing Xue (ORCID: https://orcid.org/0000-0002-4201-3817)
- Nguyen Duc Phuong (ORCID: https://orcid.org/0000-0003-3779-197X)
- Le Quoc Hung
- Le Q. Ham
Institutions
- Vietnam National University Ho Chi Minh City (VN)
- Vietnam National University, Hanoi (VN)
- Vietnam Academy of Social Sciences (VN)
- ShanghaiTech University (CN)
- The Vietnam National Institute of Educational Sciences (VN)
- Hanoi University of Science and Technology (VN)
Publication Details
- Journal
- Canadian Mathematical Bulletin
- Published
- 2025-07-14
- DOI
- https://doi.org/10.4153/s0008439525100866
- Primary Topic
- advanced mathematical theories
- Type
- article
- Field-Weighted Citation Impact
- 0.00