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Analogues of Iwasawa’s $\mu = 0$ conjecture and the weak Leopoldt conjecture for a non-cyclotomic $\mathbb{Z}_2$-extension

Choi, Junhwa ; Kezuka, Yukako ; Li, Yongxiong



Abstract

Let K = Q(root-q), where q is any prime number congruent to 7 modulo 8, and let O be the ring of integers of K. The prime 2 splits in K, say 2O = pp*, and there is a unique Z(2)-extension K-infinity of K which is unramified outside p. Let H be the Hilbert class field of K, and write H-infinity = HK infinity. Let M(H-infinity) be the maximal abelian 2-extension of H-infinity which is unramified ...

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