论恒星环的瓦林数

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2024-08-25 DOI:10.1112/mtk.12276

Tomasz Kowalczyk, Piotr Miska

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引用次数: 0

摘要

设为正整数。设是一个具有第级残差域的恒等本地环。我们用和给出了第th个瓦林数的一些上下限。在很多情况下，我们都能计算出。我们还得到了分数总环的第 th 瓦林数的类似结果。然后，我们给出了应用。特别是，对于和的任何素数，我们都能计算 .

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On Waring numbers of henselian rings

Let be a positive integer. Let be a henselian local ring with residue field of th level . We give some upper and lower bounds for the th Waring number in terms of and . In large number of cases, we are able to compute . Similar results for the th Waring number of the total ring of fractions of are obtained. We then provide applications. In particular, we compute and for and any prime .

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.