论文标题
某些有限的三维基质组的增长
Growth in Some Finite Three-Dimensional Matrix Groups
论文作者
论文摘要
我们研究了一些有限的三维基质组中产品集的生长。特别是，我们证明了关于$ 2 \ times 2 $上三角矩阵的组的两个结果：使用乘法组合物中的技术估算了产品集估算，以及使用发病率几何形状的能量估计。能量方法给出了更好的定量结果，但仅适用于小集。我们还证明了海森堡集团的能量结果。
We study the growth of product sets in some finite three-dimensional matrix groups. In particular, we prove two results about the group of $2\times 2$ upper triangular matrices over arbitrary finite fields: a product set estimate using techniques from multiplicative combinatorics, and an energy estimate using incidence geometry. The energy method gives better quantitative results, but only applies to small sets. We also prove an energy result for the Heisenberg group.
