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.


Published in:
Journal Of Number Theory, 173, 602-613
Year:
2017
Publisher:
San Diego, Elsevier
ISSN:
0022-314X
Keywords:
Laboratories:




 Record created 2017-02-17, last modified 2018-03-17


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