绝对友好的措施

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2024-05-24 DOI:10.1112/mtk.12256

Shreyasi Datta, Justin Liu

{"title":"绝对友好的措施","authors":"Shreyasi Datta, Justin Liu","doi":"10.1112/mtk.12256","DOIUrl":null,"url":null,"abstract":"In this paper, we extend the work of Pollington and Velani [Selecta Math. 11(2005)] to an <math></math>-arithmetic set-up, where <math></math> is a finite set of valuations of <math></math>. In particular, for an absolutely friendly measure <math></math> supported on a compact set in <math></math>, we give a summation condition on an approximating function <math></math> such that <math></math> almost no point in the compact set is <math></math> approximable. The crucial ingredient is a version of the simplex lemma that we prove dynamically.","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12256","citationCount":"0","resultStr":"{\"title\":\"On absolutely friendly measures on\",\"authors\":\"Shreyasi Datta, Justin Liu\",\"doi\":\"10.1112/mtk.12256\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we extend the work of Pollington and Velani [Selecta Math. 11(2005)] to an <math></math>-arithmetic set-up, where <math></math> is a finite set of valuations of <math></math>. In particular, for an absolutely friendly measure <math></math> supported on a compact set in <math></math>, we give a summation condition on an approximating function <math></math> such that <math></math> almost no point in the compact set is <math></math> approximable. The crucial ingredient is a version of the simplex lemma that we prove dynamically.\",\"PeriodicalId\":18463,\"journal\":{\"name\":\"Mathematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12256\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematika\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12256\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematika","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12256","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文将 Pollington 和 Velani [Selecta Math. 11(2005)]的工作扩展到-算术设置，其中是.的有限估值集。特别是，对于支持在.的紧凑集上的绝对友好度量，我们给出了逼近函数的求和条件，使得紧凑集上几乎没有点是可逼近的。其中的关键要素是我们用动态方法证明的一个版本的单纯形 Lemma。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On absolutely friendly measures on

In this paper, we extend the work of Pollington and Velani [Selecta Math. 11(2005)] to an -arithmetic set-up, where is a finite set of valuations of . In particular, for an absolutely friendly measure supported on a compact set in , we give a summation condition on an approximating function such that almost no point in the compact set is approximable. The crucial ingredient is a version of the simplex lemma that we prove dynamically.

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

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.