Rossmann's simple-pole conjecture for nilpotent algebra zeta functions
Let be the coefficient ring, let be an -dimensional nilpotent -algebra, and write and for its subalgebra and ideal zeta functions. Let . Rossmann's simple-pole conjecture. Both and have a simple pole at , with residue . This refines the pole-existence conjecture for nilpotent algebras; the supplied text notes that the additional nilpotence requirement is essential and gives no indication that the conjecture itself has been resolved.
References
Primary source
Tomas Reunbrouck, “p-Adic Asymptotic Subalgebra Enumeration”, arXiv:2605.20422 (2026).
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