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

2020/11/12 by Ya-Qing Hu, Hu, Ya-Qing
Engineering · Mathematics · #11C08 #11P05 #20F18 #20M14 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2011.06683

openalex publication_date 2020/11/12 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28

Abstract

Kamke \citeKamke1921 solved an analog of Waring's problem with nth powers replaced by integer-valued polynomials. Larsen and Nguyen \citeLN2019 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 \citeHu2020 to solve an analog of Waring's problem for the general discrete Heisenberg groups H_2n+1(ℤ) for any integer n≥1.

Related

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• Counting Irreducible Representations of the Discrete Heisenberg Group Over the Integers of a quadratic number field
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