论文标题
稀疏图上的总和，产品和扩张
Sums, products and dilates on sparse graphs
论文作者
论文摘要
令$ a \ subset \ mathbb r $和$ g \ subset a \ times a $。我们证明，对于任何$λ\ in \ Mathbb r \ setMinus \ { - 1,0,1 \} $，\ [\ max \ {| a+_g a+_g a |，| a+_gλa|，|，| a \ cdot_g a \ cdot_g a \ cdot_g a | \ gg} \ gg gg | g | g | g |^6/6/6/11}}。 \]
Let $A \subset \mathbb R$ and $G \subset A \times A$. We prove that, for any $λ\in \mathbb R \setminus \{-1,0,1\}$, \[ \max \{|A+_G A|, |A+_G λA|, |A\cdot_G A|\} \gg |G|^{6/11}. \]
