The zero-pole 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. Zero-pole conjecture. The topological zeta function ζ\cA,\topo(\ess)\zeta_{\cA,\topo}(\ess) has a pole at zero. This is motivated by the apparent analogous pole at zero for meromorphic continuations of local subalgebra zeta functions, although no explanation is known.

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Primary source

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

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