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On certain infinite families of imaginary quadratic fields whose Iwasawa $\lambda $-invariant is equal to 1

Volume 168 / 2015

Akiko Ito Acta Arithmetica 168 (2015), 301-339 MSC: Primary 11R11; Secondary 11R23. DOI: 10.4064/aa168-4-1

Abstract

Let $p$ be an odd prime number. We prove the existence of certain infinite families of imaginary quadratic fields in which $p$ splits and for which the Iwasawa $\lambda $-invariant of the cyclotomic $\mathbb {Z}_p$-extension is equal to $1$.

Authors

  • Akiko ItoKanagawa University
    3-27-1, Rokkakubashi, Kanagawa-ku
    Yokohama-shi, Kanagawa, 221-8686, Japan
    e-mail

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