Geodesic
A Short Remark on the Multiplicative Energy of the Spectrum
Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 444-454

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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.
Keywords: large exponential sum, multiplicative energy, sum-product phenomenon. 
@article{MZM_2019_105_3_a11,
     author = {I. D. Shkredov},
     title = {A {Short} {Remark} on the {Multiplicative} {Energy} of the {Spectrum}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {444--454},
     publisher = {mathdoc},
     volume = {105},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a11/}
}
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I. D. Shkredov. A Short Remark on the Multiplicative Energy of the Spectrum. Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 444-454. http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a11/