## Ubiquity of simplices in subsets of vector spaces over finite fields

##### 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.

##### Part of

##### Citation

arXiv:math/0703504v2