Brumer's conjecture for equivariant partial zeta values

Let $K/k$ be an Abelian extension of number fields with Galois group $G$. Let $\theta_{K/k,S}(0)$ be the value at $0$ of the $S$-imprimitive equivariant $L$-function, and let $\boldsymbol{\mu_K}$ and $\mathrm{Cl}_K$ denote the group of roots of unity and the class group of $K$, respectively. For a $\mathbb{Z}[G]$-module, write $\operatorname{Ann}_{\mathbb{Z}[G]}$ for its annihilator.

Brumer's conjecture.

$$\operatorname{Ann}_{\mathbb{Z}[G]} \mu_K\,\cdot\,\theta_{K/k,S}(0)\subseteq \operatorname{Ann}_{\mathbb{Z}[G]}\mathrm{Cl}_K.$$

This refines the integrality property for equivariant $L$-function values and generalizes the analytic class number formula. Its resolution is not established in the supplied text.