论文标题
正式laurent系列的持续分数的度量特性
Metrical properties for continued fractions of formal Laurent series
论文作者
论文摘要
由关于连续部分商的增长的实数的持续分数度量理论的最新发展的动机，我们考虑了其对正式lourent系列领域的模拟。令$ a_n（x）$为$ n $ th $ n $，在正式laurent系列领域持续扩展$ x $的部分商品。我们考虑$ x $的集合，以便$°a_ {n+1}（x）+\ cdots+°a_ {n+k}（n+k}（x）〜\ ge〜φ（n）$可用于无限的$ n $，并且分别为$ n $，并且在$ k \ ge1 $ n $ k \ ge1 $ as n integer and $ m的$ n $ ns $ n ins $ n is $ n ins $ n n n $ k \ ge1中。我们根据HAAR度量和Hausdorff维度确定这些集合的大小。
Motivated by recent developments in the metrical theory of continued fractions for real numbers concerning the growth of consecutive partial quotients, we consider its analogue over the field of formal Laurent series. Let $A_n(x)$ be the $n$th partial quotient of the continued fraction expansion of $x$ in the field of formal Laurent series. We consider the sets of $x$ such that $°A_{n+1}(x)+\cdots+°A_{n+k}(x)~\ge~Φ(n)$ holds for infinitely many $n$ and for all $n$ respectively, where $k\ge1$ is an integer and $Φ(n)$ is a positive function defined on $\mathbb{N}$. We determine the size of these sets in terms of Haar measure and Hausdorff dimension.
