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A Remark on Sets with Small Wiener Norm

  • I. D. Shkredov
Chapter
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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).

Keywords

Exponential sums Wiener norm Sum-product Multiplicative subgroups 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • I. D. Shkredov
    • 1
    • 2
    • 3
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.IITP RASMoscowRussia
  3. 3.MIPTDolgoprudniiRussia

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