Ubiquity of simplices in subsets of vector spaces over finite fields

2007/03/16 by Hart, Derrick, Iosevich, Alex
#Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0703504

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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