Abstract
We improve an estimate for the additive energy of sets \(A\) with small product \(AA\). The proof uses some properties of level sets of convolutions of the indicator function of \(A\), namely, their almost invariance under multiplication by elements of \(A\).
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Acknowledgments
The authors wish to express gratitude to T. Schoen for valuable remarks.
Funding
This work was supported by the Russian Science Foundation under grant 19-11-00001.
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Ol’mezov, K.I., Semchenkov, A.S. & Shkredov, I.D. On Popular Sums and Differences for Sets with Small Multiplicative Doubling. Math Notes 108, 557–565 (2020). https://doi.org/10.1134/S000143462009028X
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DOI: https://doi.org/10.1134/S000143462009028X