On Equivariant Dedekind Zeta-Functions at $s=1$

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.

2010 Mathematics Subject Classification: 11R42, 11R33

Keywords and Phrases: Artin $L$-functions, equivariant zeta functions, leading terms

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