Geodesic
On Sumsets of Subsets of Squares
Informatics and Automation, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 311-317

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $A\subseteq \{1,\dots ,N\}$ be a set of size $\delta N$. We prove a Bogolyubov–Ruzsa type result that $A^2+A^2+A^2-A^2-A^2-A^2$ contains a large low-dimensional generalized arithmetic progression.
Keywords: additive theorems, squares. 
@article{TRSPY_2021_314_a14,
     author = {Tomasz Schoen},
     title = {On {Sumsets} of {Subsets} of {Squares}},
     journal = {Informatics and Automation},
     pages = {311--317},
     publisher = {mathdoc},
     volume = {314},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2021_314_a14/}
}
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Tomasz Schoen. On Sumsets of Subsets of Squares. Informatics and Automation, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 311-317. http://geodesic.mathdoc.fr/item/TRSPY_2021_314_a14/