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arXiv · 2407.14624

Waring Numbers of Ramified $p$-adic Rings

Lucas Anthony·Joe Burton·Irene Deegbe·Sarah England·Spencer Hamblen·Reagan Knowles·Luke Stewart·Hannah Wright
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Abstract

Let $p$ be prime and $e,k$ be positive integers, and let $R = {\mathbb Z}_p[\sqrt[e]{p}]$. We calculate the Waring numbers $g_R(k)$ for many values of $p, e$, and $k$, and investigate how the Waring numbers for $p=2$ change as $e$ and $k$ vary.

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Lucas Anthony, Joe Burton, Irene Deegbe, Sarah England, Spencer Hamblen, Reagan Knowles, Luke Stewart, Hannah Wright. 2024-07-19. Waring Numbers of Ramified $p$-adic Rings. https://arxiv.org/abs/2407.14624

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