论文标题
总产品问题的最新信息
An update on the sum-product problem
论文作者
论文摘要
我们改善了最著名的总和估计值。 We prove that \[ \max(|A+A|,|AA|)\geq |A|^{\frac{4}{3} + \frac{2}{1167} - o(1)}\,, \] for a finite $A\subset \mathbb R$, following a streamlining of the arguments of Solymosi, Konyagin and Shkredov。我们对我们的技术包括了一些新的观察。 此外，\ [| aa+aa | \ geq | a |^{\ frac {127} {80} {80} - o（1）} \，。 \]此外，对于凸面设置$ a $，我们显示\ [| a+a | \ geq | a |^{\ frac {30} {19} {19} {19} -o（1）} \，。 \]本文在很大程度上是独立的。
We improve the best known sum-product estimates over the reals. We prove that \[ \max(|A+A|,|AA|)\geq |A|^{\frac{4}{3} + \frac{2}{1167} - o(1)}\,, \] for a finite $A\subset \mathbb R$, following a streamlining of the arguments of Solymosi, Konyagin and Shkredov. We include several new observations to our techniques. Furthermore, \[ |AA+AA|\geq |A|^{\frac{127}{80} - o(1)}\,. \] Besides, for a convex set $A$ we show that \[ |A+A|\geq |A|^{\frac{30}{19}-o(1)}\,. \] This paper is largely self-contained.
