Counting additive decompositions of quadratic residues in finite fields

Simon R. Blackburn; Sergei V. Konyagin; Igor E. Shparlinski

doi:10.7169/facm/2015.52.2.3

Counting additive decompositions of quadratic residues in finite fields

Simon R. Blackburn, Sergei V. Konyagin, Igor E. Shparlinski

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1 Citation (Scopus)

Abstract

We say that a set S is additively decomposed into two sets A and B if S = {a+b: a ∈ A, b ∈ B}. A. Sárközy has recently conjectured that the set Q of quadratic residues modulo a prime p does not have nontrivial decompositions. Although various partial results towards this conjecture have been obtained, it is still open. Here we obtain a nontrivial upper bound on the number of such decompositions.

Original language	English
Pages (from-to)	223-227
Number of pages	5
Journal	Functiones et Approximatio, Commentarii Mathematici
Volume	52
Issue number	2
DOIs	https://doi.org/10.7169/facm/2015.52.2.3
Publication status	Published - Jun 2015
Externally published	Yes

Keywords

Additive decompositions
Finite fields
Quadratic nonresidues character sums

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10.7169/facm/2015.52.2.3

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KW - Quadratic nonresidues character sums

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