论文标题
Waring在本地尼尔植物组中的问题：离散的海森伯格群体的案例
Waring's Problem For Locally Nilpotent Groups: The Case of Discrete Heisenberg Groups
论文作者
论文摘要
kamke \ cite {kamke1921}解决了沃林问题的类似物，$ n $ th powers被整数价值多项式代替。 Larsen和Nguyen \ cite {ln2019}探讨了代数群体作为Waring问题的自然环境。本文在先前的工作中开发的本地nilpotent群体中，应用多项式图和多项式序列的理论\ cite {hu2020}来解决Waring的类似物，以解决一般离散的Heisenberg组$ h_ {2n+1}（2n+1}（\ nathbb {z}）（\ nathbb {z}）$。
Kamke \cite{Kamke1921} solved an analog of Waring's problem with $n$th powers replaced by integer-valued polynomials. Larsen and Nguyen \cite{LN2019} explored the view of algebraic groups as a natural setting for Waring's problem. This paper applies the theory of polynomial maps and polynomial sequences in locally nilpotent groups developed in previous work \cite{Hu2020} to solve an analog of Waring's problem for the general discrete Heisenberg groups $H_{2n+1}(\mathbb{Z})$ for any integer $n\ge1$.
