Type: Article

The sum-product estimate for large subsets of prime fields

M. Z. Garaev;

Abstract:

Let F-p be the field of prime order p. It is known that for any integer N epsilon [1, p] one can construct a subset A subset of F-p with |A| = N such that max{|A + A|, |AA|} << p(1/2)|A|(1/2). One of the results of the present paper implies that if A subset of F-p with |A| > p(2/3), then max{|A + A|, |AA|} >> p(1/2)|A|(1/2).