On the Finite Field Cone Restriction Conjecture in Four Dimensions and Applications in Incidence Geometry
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2022-11
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Journal Article
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Abstract
The first purpose of this paper is to solve completely the finite field cone restriction conjecture in four dimensions with -1 non-square. The second is to introduce a new approach to study incidence problems via restriction theory. More precisely, using the cone restriction estimates, we will prove sharp point-sphere incidence bounds associated with complex-valued functions for sphere sets of small size. Our incidence bounds with a specific function improve significantly, a result given by Cilleruelo, Iosevich, Lund, Roche-Newton, and Rudnev.
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published
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2022 (21)
Pages / Article No.
17079 - 17111
Publisher
Oxford University Press
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03457 - Welzl, Emo (emeritus) / Welzl, Emo (emeritus)
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191067 - Erdos-Falconer Distance Conjecture and Related Topics (SNF)