An ergodic approach towards an equidistribution result of Ferrero--Washington
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909598118576128 |
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| author | Lee, Jungwon Palvannan, Bharathwaj |
| author_facet | Lee, Jungwon Palvannan, Bharathwaj |
| contents | 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 $\{0,1,2,\cdots,p-1\}^{\mathbb{Z}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_09620 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An ergodic approach towards an equidistribution result of Ferrero--Washington Lee, Jungwon Palvannan, Bharathwaj Number Theory Dynamical Systems 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 $\{0,1,2,\cdots,p-1\}^{\mathbb{Z}}$. |
| title | An ergodic approach towards an equidistribution result of Ferrero--Washington |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2207.09620 |