Waring Numbers of Ramified $p$-adic Rings

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

Waring Numbers of Ramified $p$-adic Rings

Number Theory 2025-07-08 v5

Authors: 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.

Keywords

Waring numbers ramified p-adic rings number theory prime numbers algebraic structures

Cite

@article{arxiv.2407.14624,
  title  = {Waring Numbers of Ramified $p$-adic Rings},
  author = {Lucas Anthony and Joe Burton and Irene Deegbe and Sarah England and Spencer Hamblen and Reagan Knowles and Luke Stewart and Hannah Wright},
  journal= {arXiv preprint arXiv:2407.14624},
  year   = {2025}
}

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21 pages, 5 figures

Waring Numbers of Ramified $p$-adic Rings

Abstract

Keywords

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