## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### On indivisibility of relative class numbers of totally imaginary quadratic extensions and these relative Iwasawa invariants

Yuuki Takai

#### Abstract

In this paper, we announce some results on indivisibility of relative class numbers of CM quadratic extensions $K/F$ of a fixed totally real number field $F$ which is Galois over $\mathbf{Q}$ and on vanishing of these relative Iwasawa $\lambda_{p}$-, $\mu_{p}$-invariants. In particular, we give a lower bound of the number of such CM extensions $K/F$ with bounded (norm of) relative discriminants. To prove them, we use Hilbert modular forms of half-integral weight.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 90, Number 2 (2014), 33-36.

Dates
First available in Project Euclid: 30 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.pja/1391091380

Digital Object Identifier
doi:10.3792/pjaa.90.33

Mathematical Reviews number (MathSciNet)
MR3161543

Zentralblatt MATH identifier
1286.11067

#### Citation

Takai, Yuuki. On indivisibility of relative class numbers of totally imaginary quadratic extensions and these relative Iwasawa invariants. Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 2, 33--36. doi:10.3792/pjaa.90.33. https://projecteuclid.org/euclid.pja/1391091380

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