If $\mathcal{O}$ is the ring of integers of a number field, then the Hecke-L-series for a character $\chi$ of the class group is defined as $$L(\chi,s) = \sum_{\mathfrak{a} \neq 0}\frac{\chi(\mathfrak{a})}{N(\mathfrak{a})^s}$$ with $N(\mathfrak{a}) = (\mathcal{O}:\mathfrak{a})$. Using this L-series one can proof the generalized Dirichlet density theorem (generalizes Dirichlet's theorem on primes in arithmetic progressions to primes in certain ideal classes) of whom the celebrated Cebotarev density theorem is a corollary.

Now let $D$ be a Dedekind domain $D$ with the property that $D/P$ is finite for each prime $P \subseteq D$. Then one can obviously define an L-series as above.

**Question:** Are there examples of Dedekind domains where L-series were used to prove similar density theorems as in the case of number fields ?