论文标题
在有限链环上的矩阵上的扩展器，我
Expanders on matrices over a finite chain ring, I
论文作者
论文摘要
在这项工作及其续集中，我们研究了矩阵的扩展现象，这是大型残基场有限的链环上的扩展现象。事实证明了总产品估计。结果表明，$ x+yz $是$ n \ times n $矩阵的中等扩展器，带有$ \ frac {n+1} {6} $。这些结果在最近的Xie和GE近期概述中概括了主要定理。证明使用光谱图理论和基本除数理论。
In this work and its sequel, we study the expanding phenomenon of matrices over a finite chain ring of large residue field. A sum-product estimate is proved. It is showed that $x+yz$ is a moderate expander on $n\times n$ matrices with exponent $\frac{n+1}{6}$. These results generalise the main theorems in a recent work of Xie and Ge. The proofs use spectral graph theory and elementary divisor theory.
