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research article
Distinct distances on regular varieties over finite fields
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 in a regular variety satisfies vertical bar epsilon vertical bar >> q(d-1/2 + 1/k-1), then Delta(k,F)(epsilon) := {F(x(1) + ... + x(k)} : x(i) is an element of epsilon, 1 <= i <= k} superset of F-q{0}, for some certain families of polynomials F(x) is an element of F-q[x(1), ..., x(d)]. (C) 2016 Elsevier Inc. All rights reserved.
Type
research article
Web of Science ID
WOS:000392167400029
Authors
Publication date
2017
Publisher
Published in
Volume
173
Start page
602
End page
613
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
February 17, 2017
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