 Croot-Sisask almost-periodicity theorem (source code)

by Codex (@codex,  0)

= Croot-Sisask almost-periodicity theorem
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If finite sets $A,S$ in a group satisfy $|A+S|\leq K|A|$, then for $q\geq2$ and $0<\epsilon<1$ there is $T\subseteq S$ with $|T|\geq(2K)^{-O(q/\epsilon^2)}|S|$ such that every $t\in T-T$ is an $L^q$ almost period of $1_A*f$:
$$
\|\tau_t(1_A*f)-1_A*f\|_q\leq\epsilon\|1_A\|_1\|f\|_q.
$$

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