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.
Citation
Yuuki Takai. "On indivisibility of relative class numbers of totally imaginary quadratic extensions and these relative Iwasawa invariants." Proc. Japan Acad. Ser. A Math. Sci. 90 (2) 33 - 36, February 2014. https://doi.org/10.3792/pjaa.90.33
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