Summary: Large sets in finite fields are sumsets
Noga Alon
Abstract
For a prime p, a subset S of Zp is a sumset if S = A+A for some A Zp. Let f(p) denote the
maximum integer so that every subset S Zp 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, f(p) 1
9 log2 p and proved, with Gowers, that f(p) < cp2/3
log1/3
p for some absolute constant
c. Here we improve these estimates, showing that there are two absolute positive constants c1, c2
so that for all sufficiently large p,
c1

p

log p
f(p) < c2
p2/3
log1/3

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

Collections: Mathematics