解析前p$ p$群的下p$ p$ -级数与Hausdorff维数

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-08-24 DOI:10.1112/jlms.70271

Iker de las Heras, Benjamin Klopsch, Anitha Thillaisundaram

{"title":"解析前p$ p$群的下p$ p$ -级数与Hausdorff维数","authors":"Iker de las Heras, Benjamin Klopsch, Anitha Thillaisundaram","doi":"10.1112/jlms.70271","DOIUrl":null,"url":null,"abstract":"Let <math>\n <semantics>\n <mi>G</mi>\n <annotation>$G$</annotation>\n </semantics></math> be a <math>\n <semantics>\n <mi>p</mi>\n <annotation>$p$</annotation>\n </semantics></math>-adic analytic pro-<math>\n <semantics>\n <mi>p</mi>\n <annotation>$p$</annotation>\n </semantics></math> group of dimension <math>\n <semantics>\n <mi>d</mi>\n <annotation>$d$</annotation>\n </semantics></math>, with lower <math>\n <semantics>\n <mi>p</mi>\n <annotation>$p$</annotation>\n </semantics></math>-series <math>\n <semantics>\n <mrow>\n <mi>L</mi>\n <mo>:</mo>\n <msub>\n <mi>P</mi>\n <mi>i</mi>\n </msub>\n <mrow>\n <mo>(</mo>\n <mi>G</mi>\n <mo>)</mo>\n </mrow>\n <mo>,</mo>\n <mspace></mspace>\n <mi>i</mi>\n <mo>∈</mo>\n <mi>N</mi>\n </mrow>\n <annotation>$\\mathcal {L} \\colon P_i(G), \\,i \\in \\mathbb {N}$</annotation>\n </semantics></math>. We produce an approximate series which descends regularly in strata and whose terms deviate from <math>\n <semantics>\n <mrow>\n <msub>\n <mi>P</mi>\n <mi>i</mi>\n </msub>\n <mrow>\n <mo>(</mo>\n <mi>G</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$P_i(G)$</annotation>\n </semantics></math> in a uniformly bounded way. This brings to light a new set of rational invariants <math>\n <semantics>\n <mrow>\n <msub>\n <mi>ξ</mi>\n <mn>1</mn>\n </msub>\n <mo>,</mo>\n <mtext>…</mtext>\n <mo>,</mo>\n <msub>\n <mi>ξ</mi>\n <mi>d</mi>\n </msub>\n <mo>∈</mo>\n <mrow>\n <mo>[</mo>\n <mstyle>\n <mn>1</mn>\n </mstyle>\n <mo>/</mo>\n <mi>d</mi>\n <mo>,</mo>\n <mn>1</mn>\n <mo>]</mo>\n </mrow>\n </mrow>\n <annotation>$\\xi _1, \\ldots, \\xi _d \\in [\\nicefrac {1}{d},1]$</annotation>\n </semantics></math>, canonically associated to <math>\n <semantics>\n <mi>G</mi>\n <annotation>$G$</annotation>\n </semantics></math>, such that\n\n ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 2","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70271","citationCount":"0","resultStr":"{\"title\":\"The lower \\n \\n p\\n $p$\\n -series of analytic pro-\\n \\n p\\n $p$\\n groups and Hausdorff dimension\",\"authors\":\"Iker de las Heras, Benjamin Klopsch, Anitha Thillaisundaram\",\"doi\":\"10.1112/jlms.70271\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let <math>\\n <semantics>\\n <mi>G</mi>\\n <annotation>$G$</annotation>\\n </semantics></math> be a <math>\\n <semantics>\\n <mi>p</mi>\\n <annotation>$p$</annotation>\\n </semantics></math>-adic analytic pro-<math>\\n <semantics>\\n <mi>p</mi>\\n <annotation>$p$</annotation>\\n </semantics></math> group of dimension <math>\\n <semantics>\\n <mi>d</mi>\\n <annotation>$d$</annotation>\\n </semantics></math>, with lower <math>\\n <semantics>\\n <mi>p</mi>\\n <annotation>$p$</annotation>\\n </semantics></math>-series <math>\\n <semantics>\\n <mrow>\\n <mi>L</mi>\\n <mo>:</mo>\\n <msub>\\n <mi>P</mi>\\n <mi>i</mi>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <mi>G</mi>\\n <mo>)</mo>\\n </mrow>\\n <mo>,</mo>\\n <mspace></mspace>\\n <mi>i</mi>\\n <mo>∈</mo>\\n <mi>N</mi>\\n </mrow>\\n <annotation>$\\\\mathcal {L} \\\\colon P_i(G), \\\\,i \\\\in \\\\mathbb {N}$</annotation>\\n </semantics></math>. We produce an approximate series which descends regularly in strata and whose terms deviate from <math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mi>P</mi>\\n <mi>i</mi>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <mi>G</mi>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$P_i(G)$</annotation>\\n </semantics></math> in a uniformly bounded way. This brings to light a new set of rational invariants <math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mi>ξ</mi>\\n <mn>1</mn>\\n </msub>\\n <mo>,</mo>\\n <mtext>…</mtext>\\n <mo>,</mo>\\n <msub>\\n <mi>ξ</mi>\\n <mi>d</mi>\\n </msub>\\n <mo>∈</mo>\\n <mrow>\\n <mo>[</mo>\\n <mstyle>\\n <mn>1</mn>\\n </mstyle>\\n <mo>/</mo>\\n <mi>d</mi>\\n <mo>,</mo>\\n <mn>1</mn>\\n <mo>]</mo>\\n </mrow>\\n </mrow>\\n <annotation>$\\\\xi _1, \\\\ldots, \\\\xi _d \\\\in [\\\\nicefrac {1}{d},1]$</annotation>\\n </semantics></math>, canonically associated to <math>\\n <semantics>\\n <mi>G</mi>\\n <annotation>$G$</annotation>\\n </semantics></math>, such that\\n\\n \",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":\"112 2\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-08-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70271\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70271\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70271","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

设G$ G$是维数为d$ d$的p$ p$一元解析亲p$ p$群，其下p$ p$ -级数为L：P i(G), i∈N $\mathcal {L} \冒号P_i(G), \,i \in \mathbb {N}$。我们得到了一个近似级数，它在地层中有规律地下降，其项以一致有界的方式偏离pi (G)$ P_i(G)$。这就引出了一组新的有理不变量ξ 1，…，ξ d∈[1 / d,1]$ \xi _1, \ldots, \xi _d \in [\nicefrac {1}{d},1]$，通常与G$ G$相关联，使得

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The lower

p
$p$
-series of analytic pro-

p
$p$
groups and Hausdorff dimension

查看原文本刊更多论文

The lower p $p$ -series of analytic pro- p $p$ groups and Hausdorff dimension

Let $G$ be a $p$ -adic analytic pro- $p$ group of dimension $d$ , with lower $p$ -series $L : P_{i} (G), i \in N$ . We produce an approximate series which descends regularly in strata and whose terms deviate from $P_{i} (G)$ in a uniformly bounded way. This brings to light a new set of rational invariants $ξ_{1}, …, ξ_{d} \in [1 / d, 1]$ , canonically associated to $G$ , such that

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.