It is an open problem whether the Iwasawa λ-invariants of the ${\mathbb{Z}}_p$-extensions of a fixed number field are bounded. Using the class-field theoretic tool of logarithmic class groups, we obtain bounds for the λ-invariants of ${\mathbb{Z}}_p$-extensions of suitable field extensions of imaginary quadratic number fields. We also prove the Gross-Kuz'min Conjecture for certain families of non-cyclotomic ${\mathbb{Z}}_p$-extensions.

中文翻译：

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关于岩泽λ-不变量的局部和全局边界

它是一个开放的问题是否岩泽λ的-invariants${\mathbb{ž}}_p$-固定数字字段的扩展是有界的。使用对数类组的类域理论工具，我们获得了λ-不变量的界${\mathbb{ž}}_p$-虚二次数场的合适场扩展。我们还证明了某些非环原子族的Gross-Kuz'min猜想${\mathbb{ž}}_p$-扩展名。