论文标题
离散的总产品类型问题：能源变体和应用
Discretized sum-product type problems: Energy variants and Applications
论文作者
论文摘要
在本文中，我们提供了\ [\ sum_ {c} c} | \ {（a_1，a_2，b_1，b_2）\ in A^2 \ times b^2：|（a_1 + cb_1） - （a_2 + cb_2）| nondy nondudueudueudugientr，我们提供估计的估计值。集合。我们的证明遵循Guth-Katz-Zahl方法（2021），并沿此过程中进行了适当的更改，以阐明和优化许多步骤。还将讨论几个申请。
In this paper, we provide estimates for the additive discretized energy of \[\sum_{c\in C} |\{(a_1, a_2, b_1, b_2)\in A^2\times B^2: |(a_1 +cb_1) - (a_2 + cb_2)|\le δ\}|_δ,\] that depend on non-concentration conditions of the sets. Our proof follows the Guth-Katz-Zahl approach (2021) with appropriate changes along the way clarifying and optimizing many of the steps. Several applications will also be discussed.
