Abstract
We show that any set with small Wiener norm has small multiplicative energy. It gives some new bounds for Wiener norm for sets with small product set. Also, we prove that any symmetric subset S of an abelian group has a nonzero Fourier coefficient of size Ω(|S|1∕3).
This work is supported by the Russian Science Foundation under grant 19–11–00001.
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Shkredov, I.D. (2020). A Remark on Sets with Small Wiener Norm. In: Raigorodskii, A., Rassias, M. (eds) Trigonometric Sums and Their Applications. Springer, Cham. https://doi.org/10.1007/978-3-030-37904-9_12
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DOI: https://doi.org/10.1007/978-3-030-37904-9_12
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