Geodesic
Sumsets in quadratic residues
I. D. Shkredov 1
1 Division of Algebra and Number Theory Steklov Mathematical Institute Gubkina St. 8 Moscow, Russia 119991 and Delone Laboratory of Discrete and Computational Geometry Yaroslavl' State University Sovetskaya St. 14 Yaroslavl', Russia 150000
Acta Arithmetica, Tome 164 (2014) no. 3, pp. 221-243 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We describe all sets $A \subseteq {\mathbb F}_p$ which represent the quadratic residues $R \subseteq {\mathbb F}_p$ in the sense that $R=A+A$ or $R=A\mathbin {\hat{+} }A$. Also, we consider the case of an approximate equality $R \approx A+A$ and $R \approx A\mathbin {\hat{+}} A$ and prove that $A$ is then close to a perfect difference set.
DOI : 10.4064/aa164-3-2
Keywords: describe sets subseteq mathbb which represent quadratic residues subseteq mathbb sense mathbin hat consider approximate equality approx approx mathbin hat prove close perfect difference set

I. D. Shkredov  1

1 Division of Algebra and Number Theory Steklov Mathematical Institute Gubkina St. 8 Moscow, Russia 119991 and Delone Laboratory of Discrete and Computational Geometry Yaroslavl' State University Sovetskaya St. 14 Yaroslavl', Russia 150000 
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     title = {Sumsets in quadratic residues},
     journal = {Acta Arithmetica},
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     doi = {10.4064/aa164-3-2},
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I. D. Shkredov. Sumsets in quadratic residues. Acta Arithmetica, Tome 164 (2014) no. 3, pp. 221-243. doi: 10.4064/aa164-3-2

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