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arXiv · 2409.11637

Furstenberg set problem and exceptional set estimate in prime fields: dimension two implies higher dimensions

Shengwen Gan
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Abstract

In this paper, we study in prime fields the exceptional set estimates, which can be viewed as a refinement of Marstrand's orthogonal projection theorem. Additionally, we address a Furstenberg-type problem, which is closely related. It is shown that the two-dimensional result implies all higher-dimensional results in the prime-field setting.

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Shengwen Gan. 2024-09-18. Furstenberg set problem and exceptional set estimate in prime fields: dimension two implies higher dimensions. https://arxiv.org/abs/2409.11637

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