The zero-pole conjecture for topological zeta functions of algebras

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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.

References

Primary source

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

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