Lemma 2.18.
Assuming that:
p
≥
3
prime
A
⊆
𝔽
p
n
of density
α
>
0
𝟙
sup
t
≠
0
|
𝟙
A
^
(
t
)
|
≤
𝜀
Then
the number of 3-term arithmetic progressions in
A
differs from
α
3
(
p
n
)
2
by at most
𝜀
(
p
n
)
2
.