On an upper bound of \(\lambda\)-invariants of \(\mathbb{Z}_p\)-extensions over an imaginary quadratic field. (English) Zbl 1471.11271

Murakami, Kazuaki

J. Math. Soc. Japan 71, No. 3, 1005-1026 (2019).

Summary: For an odd prime number \(p\), we give an explicit upper bound of \(\lambda\)-invariants for all \(\mathbb{Z}_p\)-extensions of an imaginary quadratic field \(k\) under several assumptions. We also give an explicit upper bound of \(\lambda\)-invariants for all \(\mathbb{Z}_p\)-extensions of \(k\) in the case where the \(\lambda\)-invariant of the cyclotomic \(\mathbb{Z}_p\)-extension of \(k\) is equal to 3.

MSC:

11R23	Iwasawa theory
11R11	Quadratic extensions

Keywords:

Iwasawa invariant; \(\mathbb{Z}_p\)-extension; \(\mathbb{Z}_p^2\)-extension; imaginary quadratic field

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