某些类型$p$一元Duffin-Schaeffer集合的可实现测度

IF 0.3 4区数学 Q4 MATHEMATICS

Mathematica Scandinavica Pub Date : 2023-10-26 DOI:10.7146/math.scand.a-139832

Laursen, Mathias Løkkegaard

引用次数: 0

摘要

本文解决了最近关于用丢番图近似定义的一组集的$p$进Haar测度的猜想。这是通过确定每个家庭的测量值的频谱，并看到这与相应的猜想相矛盾来完成的。

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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Attainable measures for certain types of $p$-adic Duffin-Schaeffer sets

This paper settles recent conjectures concerning the $p$-adic Haar measure applied to a family of sets defined in terms of Diophantine approximation. This is done by determining the spectrum of measure values for each family and seeing that this contradicts the corresponding conjectures.

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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.