In *Fonctions L p-adiques des corps quadratiques imaginaires et de leurs extensions abéliennes*, 
J. Reine Angew. Math. 358 (1985), 76–91, Roland Gillard shows the following result (I mainly follow the MR review here):


Let $K$ be an imaginary quadratic field and let $p > 3$ be a prime number which splits in K into 
$(p)=\mathfrak{p}\mathfrak{p'}$. Let $K\_{\infty}$ be the unique $\mathbb{Z}\_{p}$-extension of $K$ unramified outside $\mathfrak{p}$ (thus noncyclotomic). Let $F$ be a finite abelian extension of $K$ and let $M$ be the maximal abelian $p$-extension of $F$ unramified outside $\mathfrak{p}$. Then Theorem 3.4 states that $\mathrm{Gal}(M/FK\_{\infty})$ is $\mathbb{Z}\_{p}$-torsion-free; in particular its $\mu$-invariant is 0.


Question: does anyone know if the vanishing of this $\mu$-invariant is also proven somewhere when $p=3$ (even special cases would be of interest)?


Note: with some work, you can get a PDF of the article in question without a subscription by following the link from here: <http://www.ams.org/dmr/JournalListJ.html>



Vanishing of certain $\mu$-invariants attached to abelian extensions of imaginary quadratic fields
The question has now been answered by this preprint: <http://arxiv.org/abs/1311.3565>


