## On equivariant Dedekind zeta-functions at $s=1$

### Summary

We study a refinement of an explicit conjecture of Tate concerning the values at $s=1$ of Artin $L$-functions. We reinterpret this refinement in terms of Tamagawa number conjectures and then use this connection to obtain some important (and unconditional) evidence for our conjecture.

11R42, 11R33

### Keywords/Phrases

Artin $L$-functions, equivariant zeta functions, equivariant Tamagawa number conjecture, leading terms