Sums, products and dilates on sparse graphs

2020/10/05 by Roche-Newton, Oliver
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2010.02050

Abstract

Let A ⊂ \mathbb R and G ⊂ A × A. We prove that, for any λ∈ \mathbb R ∖ \-1,0,1\, max \|A+_G A|, |A+_G λA|, |A⋅_G A|\ ≫ |G|^6/11.

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