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arXiv · 2208.09841

Pinned simplices and connections to product of sets on paraboloids

Alex Iosevich·Quy Pham·Thang Pham·Chun-Yen Shen
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Abstract

In this paper we obtain improved dimensional thresholds for dot product sets corresponding to compact subsets of a paraboloid. As a direct application of these estimates, we obtain significant improvements to the best known dimensional thresholds that guarantee that a given compact subset of Euclidean space determines a positive proportion of all possible congruence classes of simplexes. In many regimes this improves the results previously obtained by Erdogan-Hart-Iosevich (\cite{EHI}), Greenleaf-Iosevich-Liu-Palsson (\cite{GILP}) and others.

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Alex Iosevich, Quy Pham, Thang Pham, Chun-Yen Shen. 2022-08-21. Pinned simplices and connections to product of sets on paraboloids. https://arxiv.org/abs/2208.09841

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