Ernie Croot

A weighted entropy approach for the quadratic inverse large sieve conjecture

The quadratic inverse large sieve problem predicts that the examples sharp at the square-root threshold are essentially quadratic. Hanson proved the first unconditional result in this direction: if $A\subseteq[N]$, $|A|\gg\sqrt N$, and $|A_p|\le p/2+O(1)$ for every prime $p$, then $A$ contains $\gg\log N$ elements in t...