{"title":"素域中的福斯滕伯格集合问题和特殊集合估计：维数二意味着维数更高","authors":"Shengwen Gan","doi":"arxiv-2409.11637","DOIUrl":null,"url":null,"abstract":"We study Furstenberg set problem, and exceptional set estimate for\nMarstrand's orthogonal projection in prime fields for all dimensions. We define\nthe Furstenberg index $\\mathbf{F}(s,t;n,k)$ and the Marstrand index\n$\\mathbf{M}(a,s;n,k)$. It is shown that the two-dimensional result for Furstenberg set problem\nimplies all higher dimensional results.","PeriodicalId":501407,"journal":{"name":"arXiv - MATH - Combinatorics","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Furstenberg set problem and exceptional set estimate in prime fields: dimension two implies higher dimensions\",\"authors\":\"Shengwen Gan\",\"doi\":\"arxiv-2409.11637\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study Furstenberg set problem, and exceptional set estimate for\\nMarstrand's orthogonal projection in prime fields for all dimensions. We define\\nthe Furstenberg index $\\\\mathbf{F}(s,t;n,k)$ and the Marstrand index\\n$\\\\mathbf{M}(a,s;n,k)$. It is shown that the two-dimensional result for Furstenberg set problem\\nimplies all higher dimensional results.\",\"PeriodicalId\":501407,\"journal\":{\"name\":\"arXiv - MATH - Combinatorics\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11637\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11637","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Furstenberg set problem and exceptional set estimate in prime fields: dimension two implies higher dimensions
We study Furstenberg set problem, and exceptional set estimate for
Marstrand's orthogonal projection in prime fields for all dimensions. We define
the Furstenberg index $\mathbf{F}(s,t;n,k)$ and the Marstrand index
$\mathbf{M}(a,s;n,k)$. It is shown that the two-dimensional result for Furstenberg set problem
implies all higher dimensional results.
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