论文标题
关于Henselian戒指的警告数量
On Waring numbers of henselian rings
论文作者
论文摘要
让$ n> 1 $成为一个积极的整数。让$ r $为Henselian本地环，带有残留域$ k $ n $ n $ th Level $ s_n（k）$。我们为$ w_n（k）$和$ s_n（k）$的$ n $ th Waring Number $ w_n（r）$提供了一些上限和下限。在大量情况下，我们能够计算$ W_N（R）$。获得了$ r $分数的总圆环的$ n $ th Waring数量的类似结果。然后，我们提供申请。特别是我们计算$ w_n（\ mathbb {z} _p）$和$ w_n（\ mathbb {q} _p）$ for $ n \ in \ in \ {3,4,5 \} $和任何prime $ p $。
Let $n>1$ be a positive integer. Let $R$ be a henselian local ring with residue field $k$ of $n$th level $s_n(k)$. We give some upper and lower bounds for the $n$th Waring number $w_n(R)$ in terms of $w_n(k)$ and $s_n(k)$. In large number of cases we are able to compute $w_n(R)$. Similar results for the $n$th Waring number of the total ring of fractions of $R$ are obtained. We then provide applications. In particular we compute $w_n(\mathbb{Z}_p)$ and $w_n(\mathbb{Q}_p)$ for $n\in\{3,4,5\}$ and any prime $p$.
