Geodesic
Sumsets in quadratic residues
I. D. Shkredov1
1Division 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

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

DOI

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 
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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     title = {Sumsets in quadratic residues},
     journal = {Acta Arithmetica},
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     doi = {10.4064/aa164-3-2},
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