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| On a theorem of Mattila in the p-adic setting | |
| 2025-02-09 | |
| 状态 | 已发表 |
| 摘要 | Let $A, B$ be subsets of $(mathbb{Z}/p^rmathbb{Z})^2$. 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 $gin SO_2(mathbb{Z}/p^rmathbb{Z})$. 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. |
| 语种 | 英语 |
| DOI | arXiv:2502.05818 |
| 相关网址 | 查看原文 |
| 出处 | Arxiv |
| 收录类别 | PPRN.PPRN |
| WOS记录号 | PPRN:121321865 |
| WOS类目 | Mathematics |
| 资助项目 | Vietnam National Foundation for Science and Technology Development (NAFOSTED)[101.99–2021.09] |
| 文献类型 | 预印本 |
| 条目标识符 | https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/507019 |
| 专题 | 数学科学研究所 数学科学研究所_PI研究组(P)_薛博卿组 |
| 通讯作者 | Xue, Boqing |
| 作者单位 | 1.ShanghaiTech Univ, Inst Math Sci, Shanghai, Peoples R China 2.Vietnam Natl Univ, Univ Sci, Hanoi, Vietnam 3.Hanoi Univ Sci & Technol, Hanoi, Vietnam 4.Vietnam Inst Educ Sci, Hanoi, Vietnam 5.Peoples Secur Acad, Hanoi, Vietnam |
| 推荐引用方式 GB/T 7714 | Xue, Boqing,Pham, Thang,Hung, Le Q.,et al. On a theorem of Mattila in the p-adic setting. 2025. |
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