A note on Green-Shkredov's argument about two-dimensional corners in finite field
LI Guoquan · Journal of Tianjin Normal University · 2010
p is a prime,and Fp is denoted as the finite field with p elements.For an integer n1,Fnp is a vector space of n dimension over Fp.Using a definite dichotomy between structure and randomness principle,the result obtained by B.Green et al is developed as follows: e0,■Cp,e≥0,s.t.n∈N+,r∠(Fnp)≤C|Fn|2/(ln ln|Fpn|)1/(23+e),where r∠(Fnp)■max {|A|:A■Fnp×Fnp,A does not contain nontrivial triple}.