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arXiv · 2011.06683

Waring's Problem For Locally Nilpotent Groups: The Case of Discrete Heisenberg Groups

Ya-Qing Hu
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Abstract

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 $n\ge1$.

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Ya-Qing Hu. 2020-11-12. Waring's Problem For Locally Nilpotent Groups: The Case of Discrete Heisenberg Groups. https://arxiv.org/abs/2011.06683

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