Large sets in finite fields are sumsets Original Research Article

For a prime p, a subset S of Zp is a sumset if S=A+A for some Asubset ofZp. Let f(p) denote the maximum integer so that every subset Ssubset ofZp of size at least p−f(p) is a sumset. The question of determining or estimating f(p) was raised by Green. He showed that for all sufficiently large p, image and proved, with Gowers, that f(p)