TY - EJOUR
DO - 10.1016/j.jnt.2016.10.003
AB - 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.
T1 - Distinct distances on regular varieties over finite fields
DA - 2017
AU - Do, Duy Hieu
AU - Pham, Van Thang
JF - Journal Of Number Theory
SP - 602-613
VL - 173
EP - 602-613
PB - Elsevier
PP - San Diego
ID - 225792
KW - Finite fields
KW - Distinct distances
KW - Variety
KW - Diagonal polynomials
SN - 0022-314X
ER -