Finding

Paper

Abstract

We prove a query complexity variant of the weak polynomial Freiman-Ruzsa conjecture in the following form. For any $\epsilon > 0$, a set $A \subset \mathbb{Z}^d$ with doubling $K$ has a subset of size at least $K^{-\frac{4}{\epsilon}}|A|$ with coordinate query complexity at most $\epsilon \log_2 |A|$. We apply this structural result to give a simple proof of the ``few products, many sums'' phenomenon for integer sets. The resulting bounds are explicit and improve on the seminal result of Bourgain and Chang.

Authors

Dmitrii Zhelezov, Domotor P'alvolgyi

Journal

Advances in Mathematics

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