丢番图指数几何

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.4213/rm10089e

Oleg Nikolaevich German

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引用次数: 0

摘要

丢芬图指数是欧几里得空间线性子空间近似性质的最简单的定量特征。本文旨在描述丢番图近似领域的现状，即研究丢番图指数及其满足的关系。我们讨论了在整数点上用若干线性形式的值的集合逼近零问题中出现的经典丢番图指数，它们在带权的丢番图近似中的类似物，乘法丢番图指数，以及格的丢番图指数。我们特别注意移情原则。参考书目:99个标题。

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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Geometry of Diophantine exponents

Diophantine exponents are some of the simplest quantitative characteristics responsible for the approximation properties of linear subspaces of a Euclidean space. This survey is aimed at describing the current state of the area of Diophantine approximation that studies Diophantine exponents and relations they satisfy. We discuss classical Diophantine exponents arising in the problem of approximating zero with the set of the values of several linear forms at integer points, their analogues in Diophantine approximation with weights, multiplicative Diophantine exponents, and Diophantine exponents of lattices. We pay special attention to the transference principle. Bibliography: 99 titles.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.