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arXiv · 2207.09620

An ergodic approach towards an equidistribution result of Ferrero--Washington

Jungwon Lee·Bharathwaj Palvannan
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Abstract

An important ingredient in the Ferrero--Washington proof of the vanishing of cyclotomic $\mu$-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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Jungwon Lee, Bharathwaj Palvannan. 2022-07-20. An ergodic approach towards an equidistribution result of Ferrero--Washington. https://arxiv.org/abs/2207.09620

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