The $\tau$-twisted Dedekind conjecture for extensions of global fields

Let $E/F$ be an extension of global fields, and let $\tau$ be as in the preceding notation. Write $N_{E/F}$ for the relative norm and let $\Lambda_E(s,\tau\circ N_{E/F})$ and $\Lambda_F(s,\tau)$ denote the corresponding completed $L$-functions. $\tau$-twisted Dedekind conjecture. The quotient

$$\frac{\Lambda_E(s,\tau\circ N_{E/F})}{\Lambda_F(s,\tau)}$$

is holomorphic when $s\neq 1$. This is a twisted form of Dedekind's conjecture on the holomorphy of the quotient of Dedekind zeta functions; the supplied context identifies it as a long-standing conjectural implication related to holomorphy of adjoint $L$-functions, but does not establish its resolution.