函数与两个等差数列同时平铺

IF 1.5 1区数学 Q1 MATHEMATICS

Proceedings of the London Mathematical Society Pub Date : 2023-10-24 DOI:10.1112/plms.12570

Mark Mordechai Etkind, Nir Lev

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引用次数: 1

摘要

摘要:本文通过两个等差数列，在相应的平铺层和平铺层上，同时考虑了平铺层上的可测函数。我们对两个主要问题感兴趣:平铺水平的可能值是什么，以及支持的最小可能度量是什么?我们得到了一个清晰的结果，表明答案取决于和的算术性质，特别是取决于数是否理性独立。

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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Functions tiling simultaneously with two arithmetic progressions

Abstract We consider measurable functions on that tile simultaneously by two arithmetic progressions and at respective tiling levels and . We are interested in two main questions: what are the possible values of the tiling levels , and what is the least possible measure of the support of ? We obtain sharp results which show that the answers depend on arithmetic properties of and , and in particular, on whether the numbers are rationally independent or not.

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来源期刊

Proceedings of the London Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Proceedings of the London Mathematical Society is the flagship journal of the LMS. It publishes articles of the highest quality and significance across a broad range of mathematics. There are no page length restrictions for submitted papers. The Proceedings has its own Editorial Board separate from that of the Journal, Bulletin and Transactions of the LMS.