The root-location conjecture for topological zeta functions of algebras

Let $\cA$ be a non-associative $\fo$-algebra that is free of rank $d$ as an $\fo$-module, where $\fo$ is the ring of integers in a number field $k$. Root-location conjecture. If $s\in\CC$ satisfies

$$\zeta_{\cA,\topo}(s)=0,$$

then $0<\Real(s)<d-1$. The lower bound would imply alternating signs in the numerator of the rational function $\zeta_{\cA,\topo}(\ess)$; the stated upper bound is known to be pessimistic in the examples available to the author.