论文标题
局部紧凑型组的多项式图的分布良好
Well-distribution of Polynomial maps on locally compact groups
论文作者
论文摘要
Weyl的经典等分定理指出，除非所有非恒定系数都是合理的，否则实价的多项式序列是均匀分布的模量1。如果在任何$ d+1 $差异运算符下消失，则两个拓扑组之间的连续函数最多称为$ d $的\ emph {polyenmial映射}。莱布曼（Leibman）以及随后的绿色和道（Green and Tao）对多项式序列进行了表达和证明的等分定理，这些序列在nilmanifold中采用值。我们制定并证明了从局部紧凑型组到紧凑的Abelian组的多项式图的一些一般等分定理。
Weyl's classical equidistribution theorem states that real-valued polynomial sequences are uniformly distributed modulo 1, unless all non-constant coefficients are rational. A continuous function between two topological groups is called a \emph{polynomial map} of degree at most $d$ if it vanishes under any $d+1$ difference operators. Leibman, and subsequently Green and Tao, formulated and proved equidistribution theorems about polynomial sequences that take values in a nilmanifold. We formulate and prove some general equidistribution theorems regarding polynomial maps from a locally compact group into a compact abelian group.
