Balazard's conjecture on reciprocals of decomposition primes in abelian extensions

Let $K$ be a global field, and let $L/K$ be an abelian extension of degree $n$. Write $\operatorname{Dec}(L/K)$ for the set of places of $K$ that split completely in $L$. Balazard's conjecture. There exists a constant $M$ depending only on $K$ such that

$$\left|\sum_{\substack{\mathfrak{p}\in \operatorname{Dec}(L/K),\\ \operatorname{N}\mathfrak{p}\leq x}}\frac{1}{\operatorname{N}\mathfrak{p}}-\frac{1}{n}\log\log x\right|\leq M.$$

This conjecture predicts a uniform Mertens-type estimate for completely split primes in abelian extensions, generalizing the corresponding result for rational primes in arithmetic progressions and cyclotomic extensions. The supplied text gives no resolution, so the conjecture remains open.