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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 314, Pages 311–317
DOI: https://doi.org/10.4213/tm4197 (Mi tm4197) 		 
On Sumsets of Subsets of Squares

Tomasz Schoen

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland
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DOI: https://doi.org/10.4213/tm4197
Abstract: 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.
Received: July 13, 2020
Revised: February 26, 2021
Accepted: May 10, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 314, Pages 300–306
DOI: https://doi.org/10.1134/S0081543821040155
Bibliographic databases:
Document Type: Article
UDC: 511.178
MSC: primary 11P99, secondary 05D10
Language: Russian
Citation: Tomasz Schoen, “On Sumsets of Subsets of Squares”, Analytic and Combinatorial Number Theory, Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 314, Steklov Math. Inst., Moscow, 2021, 311–317; Proc. Steklov Inst. Math., 314 (2021), 300–306
Citation in format AMSBIB
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\paper On Sumsets of Subsets of Squares
\inbook Analytic and Combinatorial Number Theory
\bookinfo Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 314
\pages 311--317
\publ Steklov Math. Inst.
\publaddr Moscow
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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