论文标题
间隔良好的估计值
A Sum-Product Estimate for Well Spaced Sets
论文作者
论文摘要
我们研究了间隔良好的集合的$δ$ distrutized汇总估计值。 Our main result is: for a fixed $α\in(1,\frac{3}{2}]$, we prove that for any $\sim|A|^{-1}$-separated set $A\subset[1,2]$ and $δ=|A|^{-α}$, we have: $\mathcal{N}(A+A, δ)\cdot \ Mathcal {n}（aa，δ）\gtrsim_ε| a |δ^{ - 1+ε} $。
We study the $δ$-discretized sum-product estimates for well spaced sets. Our main result is: for a fixed $α\in(1,\frac{3}{2}]$, we prove that for any $\sim|A|^{-1}$-separated set $A\subset[1,2]$ and $δ=|A|^{-α}$, we have: $\mathcal{N}(A+A, δ)\cdot \mathcal{N}(AA, δ) \gtrsim_ε|A|δ^{-1+ε}$.
