Under the condition 100K^2 δ ≤ 1, a set with small doubling and small Fourier coefficients must have a dense intersection with a translate of a large regular Bohr set of controlled dimension.
On certain other sets of integers
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We show that if A is a subset of {1,...,N} containing no non-trivial three-term arithmetic progressions then |A|=O(N/ log^{3/4-o(1)} N).
citation-role summary
background 1
citation-polarity summary
fields
math.CO 1years
2024 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
On Fourier coefficients of sets with small doubling
Under the condition 100K^2 δ ≤ 1, a set with small doubling and small Fourier coefficients must have a dense intersection with a translate of a large regular Bohr set of controlled dimension.