论文标题
在Gauss-Kuzmin-lévy的问题上，对于最近的整数持续分数
On the Gauss-Kuzmin-Lévy problem for nearest integer continued fractions
论文作者
论文摘要
此注释提供了与最近的整数持续分数相关的某些高斯类型转移的高斯 - kuzmin-lévy问题的有效限制，作用于间隔$ i_0 = [0，\ frac {1} {2} {2} {2} {2} {2}] $或$ i_0 = [ - \ frac { - \ frac {1} {1} {2} {2} {2} {2}对于此类转换$ t $ $ i_0 $，$ q = 0.288 $小于固定常数$ q_w = 0.3036 \ ldots $
This note provides an effective bound in the Gauss-Kuzmin-Lévy problem for some Gauss type shifts associated with nearest integer continued fractions, acting on the interval $I_0=[0,\frac{1}{2}]$ or $I_0=[-\frac{1}{2},\frac{1}{2}]$. We prove asymptotic formulas $λ(T^{-n}I) =μ(I)(\vert I_0 \vert +O(q^n))$ for such transformations $T$, where $λ$ is the Lebesgue measure on $\mathbb R$, $μ$ the normalized $T$-invariant Lebesgue absolutely continuous measure, $I$ subinterval in $I_0$, and $q=0.288$ is smaller than the Wirsing constant $q_W=0.3036\ldots$
