Distinct distances on regular varieties over finite fields

2016/08/23 by Pham Van Thang, Van Thang, Pham, Do Duy Hieu +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1608.06401

arxiv created 2016/08/23 · arxiv updated 2016/08/24

Abstract

In this paper we study some generalized versions of a recent result due to Covert, Koh, and Pi (2015). More precisely, we prove that if a subset E in a regular variety satisfies |E|≫ q^{(d-1)/(2)+(1)/(k-1)}, then Δ_{k, F}(E)⊇ \mathbbF_q∖ \0\ for some certain families of polynomials F(x)∈ \mathbbF_q[x₁, …, x_d].

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