论文标题
FERRERO的等均分配结果的崇高方法-Washington
An ergodic approach towards an equidistribution result of Ferrero--Washington
论文作者
论文摘要
Ferrero中的一个重要成分 - 库博塔 - 库博塔 - leopoldt $ p $ p $ -adic $ l $ functions消失的循环$ $ $ $ $ invariant的重要成分是他们使用Weyl Criterion确定的等分分配结果。我们手稿的目的是通过采用动态方法来提供替代的证据。我们方法的关键要素是在$ \ mathbb {z} _p \ times [0,1] $上研究梯形偏斜的产物图，然后将其适当地识别为$ 2 $ 2 $的伯努尔在样本空间上的伯诺利变化的因素，{0,1,1,2，\ cdots p {0,1,2，\ cdots p-cdots，p-1} $ {
An important ingredient in the Ferrero--Washington proof of the vanishing of cyclotomic $μ$-invariant for Kubota--Leopoldt $p$-adic $L$-functions is an equidistribution result which they established using the Weyl criterion. The purpose of our manuscript is to provide an alternative proof by adopting a dynamical approach. A key ingredient to our methods is studying an ergodic skew-product map on $\mathbb{Z}_p \times [0,1]$, which is then suitably identified as a factor of the $2$-sided Bernoulli shift on the sample space $\{0,1,2,\cdots,p-1\}^{\mathbb{Z}}$.
