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Ubiquity of simplices in subsets of vector spaces over finite fields

Derrick Hart·Alex Iosevich
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Abstract

We prove that a sufficiently large subset of the $d$-dimensional vector space over a finite field with $q$ elements, $ {\Bbb F}_q^d$, contains a copy of every $k$-simplex. Fourier analytic methods, Kloosterman sums, and bootstrapping play an important role.

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Derrick Hart, Alex Iosevich. 2007-10-11. Ubiquity of simplices in subsets of vector spaces over finite fields. https://arxiv.org/abs/math/0703504

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