The root-location conjecture for topological zeta functions of algebras

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

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

then 0<\Real(s)<d10<\Real(s)<d-1. The lower bound would imply alternating signs in the numerator of the rational function ζ\cA,\topo(\ess)\zeta_{\cA,\topo}(\ess); the stated upper bound is known to be pessimistic in the examples available to the author.

Sources & referencesView supporting material

Primary source

Tobias Rossmann, “Computing topological zeta functions of groups, algebras, and modules, I”, arXiv:1405.5711 (2014).

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