论文标题
与两个算术进程同时铺平功能
Functions tiling simultaneously with two arithmetic progressions
论文作者
论文摘要
我们考虑$ \ Mathbb {r} $上的可测量函数$ f $，同时由两个算术进度同时使用$α\ mathbb {z} $和$β\ mathbb {z} $在相应的瓷砖水平$ p $和$ q $上。我们对两个主要问题感兴趣：平铺级别$ p，q $的可能值是什么，对$ f $的支持的最小程度是什么？我们获得了尖锐的结果，这些结果表明答案取决于$α，β$和$ p，q $的算术特性，尤其是$α，β$是否合理独立。
We consider measurable functions $f$ on $\mathbb{R}$ that tile simultaneously by two arithmetic progressions $α\mathbb{Z}$ and $β\mathbb{Z}$ at respective tiling levels $p$ and $q$. We are interested in two main questions: what are the possible values of the tiling levels $p,q$, and what is the least possible measure of the support of $f$? We obtain sharp results which show that the answers depend on arithmetic properties of $α, β$ and $p,q$, and in particular, on whether the numbers $α, β$ are rationally independent or not.
