Dedekind's conjecture on zeta-function quotients

Let $L/k$ be a finite algebraic extension of number fields, and let $\zeta_L(s)$ and $\zeta_k(s)$ denote their Dedekind zeta functions. Dedekind's conjecture. The quotient

$$\frac{\zeta_L(s)}{\zeta_k(s)}$$

is entire. The normal-extension case is the Aramata–Brauer theorem, while the general algebraic-extension statement is presented as a conjecture.