Green's Open Problems #83

### What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.83

Describe the rough structure of sets $A \subset \mathbb{Z}$ with $|A| = n$ and $\lVert \hat{1}\_A \rVert\_1 \leq K \log n$.

### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)

* ams-11
* ams-42

### Choose either option
- [ ] I plan on adding this conjecture to the repository
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start by reading problem 83 in the linked Green open-problems PDF, then inspect the repository's existing formalized conjectures for its conventions. Done means adding a corresponding Lean statement to the repository, with its AMS categories recorded as shown in the issue.

Written by the indexing model from the issue text.