English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $p$ be a prime number and let $d\in \mathbb{Z}_{>0}$. In this paper,following the analogy between knots and primes, we study the $p$-torsion growthin a compatible system of $(\mathbb{Z}/p^n\mathbb{Z})^d$-covers of 3-manifoldsand establish several analogues of Cuoco--Monsky's multivariable versions ofIwasawa's class number formula. Our main goal is to establish the Cuoco--Monskytype formula for branched covers of links in rational homology 3-spheres. Inaddition, we prove the precise formula over integral homology 3-spheresprompted by Greenberg's conjecture. We also obtain results on reduced Alexanderpolynomials and on the Betti number periodicity. Furthermore, we investigatethe twisted Whitehead links in $S^3$ and point out that the Iwasawa$\mu$-invariant of a $\mathbb{Z}_p^{\,2}$-cover can be an arbitrarynon-negative integer. We also calculate the Iwasawa $\mu$ and$\lambda$-invariants of all links in Rolfsen's table.

The Iwasawa invariants of $\mathbb{Z}_p^{\,d}$-covers of links