Ferrero-Washington等分布结果的遍历性研究
An ergodic approach towards an equidistribution result of Ferrero--Washington
摘要：
费雷罗-华盛顿证明分圆$μ$ -不变量为久保田-利奥波德$p$ -进$L$ -功能消失的一个重要组成部分是一个等分布的结果，他们建立了使用外尔准则。我们的手稿的目的是通过采用动态方法提供另一种证明。我们的方法的一个关键成分是研究$\mathbb{Z}_p \times [0,1]$上的遍历斜积映射，然后将其适当地识别为样本空间$\{0,1,2,\cdots,p-1\}^{\mathbb{Z}}$上的$2$侧伯努利移位的因子。
英文摘要：
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 $\{0,1,2,\cdots,p-1\}^{\mathbb{Z}}$.
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