Geodesic
Energies and structure of additive sets
Shkredov Ilya1
1Steklov Mathematical Institute
The electronic journal of combinatorics, Tome 21 (2014) no. 3
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In this paper we prove that any sumset or difference set has large $\textsf{E}_3$ energy. Also, we give a full description of families of sets having critical relations between some kind of energies such as $\textsf{E}_k$, $\textsf{T}_k$ and Gowers norms. In particular, we give criteria for a set to be a set of the form $H\dotplus \Lambda$, where $H+H$ is small and $\Lambda$ has "random structure",set equal to a disjoint union of sets $H_j$ each with small doubling,set having a large subset $A'$ with $2A'$ equal to a set with small doubling and $|A'+A'| \approx |A|^4 / \textsf{E}(A)$.
DOI : 10.37236/4369
Classification : 11B13, 11B30
Mots-clés : additive combinatorics, sumsets, energies

Shkredov Ilya  1

1 Steklov Mathematical Institute 
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     title = {Energies and structure of additive sets},
     journal = {The electronic journal of combinatorics},
     year = {2014},
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     doi = {10.37236/4369},
     zbl = {1301.11010},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4369/}
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Shkredov Ilya. Energies and structure of additive sets. The electronic journal of combinatorics, Tome 21 (2014) no. 3. doi: 10.37236/4369

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