The degree 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. Degree conjecture.

deg⁡\ess(ζ\cA,\topo(\ess))=−d.\deg_{\ess}\bigl(\zeta_{\cA,\topo}(\ess)\bigr)=-d.

This is proposed without further assumptions on \cA\cA, based on experimental evidence for k=\QQk=\QQ; unlike topological zeta functions of polynomials, the degree here is conjectured to depend only on the module rank.

References

Primary source

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

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