Mathematical Notes

, Volume 105, Issue 3–4, pp 449–457 | Cite as

A Short Remark on the Multiplicative Energy of the Spectrum

  • I. D. ShkredovEmail author


An upper bound for the multiplicative energy of the spectrum of an arbitrary subset of \(\mathbb{F}_{p}\) is obtained. Apparently, at present, this is the best bound.


large exponential sum multiplicative energy sum-product phenomenon 


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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