The Ramanujan Journal

, Volume 46, Issue 2, pp 357–372 | Cite as

A note on the size of the set \(\varvec{A^2+A}\)

  • Norbert Hegyvári
  • François Hennecart


Let \(F(x,y,z)=xy+z\). We consider some properties of expansion of the polynomial F in different settings, namely in the integers and in prime fields. The main results concern the question of covering \(\{0,1,\ldots , N\}\) (resp. \(\mathbf {F}_p\)) by \(A^2+A\) with some thin sets A.


Covering polynomial Expander Sum-product 

Mathematics Subject Classification

11B75 20G40 



We warmly thank the referee for pointing out various improvements in our results and their proofs.


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Authors and Affiliations

  1. 1.ELTE TTK, Institute of MathematicsEötvös UniversityBudapestHungary
  2. 2.Univ Lyon, UJM-Saint-Étienne, CNRS, ICJ UMR 5208Saint-ÉtienneFrance

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