论文标题
Hausdorff尺寸的数字集，具有较大的Lüroth元素
Hausdorff dimension of sets of numbers with large Lüroth elements
论文作者
论文摘要
像常规的持续分数一样，吕伦（Lüroth）系列提供了一个有趣的识别，可以用无限的整数序列来识别。这些序列根据数量的生长具有深度算术和测量理论特性。尽管不同，但常规的持续分数和Lüroth系列具有多个属性。在本文中，我们通过估计Lüroth扩展以确定的速率增长的实数亚集的Hausdorff尺寸来探讨一个相似性。这是Y. Sun和J. Wu的结果延伸到Lüroth系列的背景。 Y. Feng，B。Tan和Q.-L。最近显示了它。周，我们的主要定理中的下限实际上是一个平等。
Lüroth series, like regular continued fractions, provide an interesting identification of real numbers with infinite sequences of integers. These sequences give deep arithmetic and measure-theoretic properties of subsets of numbers according to their growth. Although different, regular continued fractions and Lüroth series share several properties. In this paper, we explore one similarity by estimating the Hausdorff dimension of subsets of real numbers whose Lüroth expansion grows at a definite rate. This is an extension of a result of Y. Sun and J. Wu to the context of Lüroth series. It was recently shown by Y. Feng, B. Tan, and Q.-L. Zhou that the lower bound in our main theorem is actually an equality.
