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 Acta Arith., 2014, Volume 164, Issue 3, Pages 221–243 (Mi acta1)

I. D. Shkredovab

a Division of Algebra and Number Theory, Steklov Mathematical Institute, Gubkina St. 8, Moscow, Russia 119991
b Delone Laboratory of Discrete and Computational Geometry, Yaroslavl' State University, Sovetskaya St. 14, Yaroslavl', Russia 150000

Abstract: 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 $R=A\hat{+}A$. Also, we consider the case of an approximate equality $R\approx A+A$ and $R\approx A\hat{+}A$ and prove that $A$ is then close to a perfect difference set.

 Funding Agency Grant Number Russian Foundation for Basic Research 11-01-0075912-01-33080 Ministry of Education and Science of the Russian Federation 11.G34.31.00532519.2012.1 This work was supported by grant RFFI NN 11-01-00759, Russian Government project 11.G34.31.0053, Federal Program "Scientific and scientific-pedagogical staff of innovative Russia" 2009-2013, grant mol_a_ved 12-01-33080 and grant Leading Scientific Schools N 2519.2012.1.

DOI: https://doi.org/10.4064/aa164-3-2

Bibliographic databases:

Document Type: Article
MSC: 11B13, 11B50, 11B75
Language: English