We present a conjectured formula for the representation zeta function of the Heisenberg group over $\mathcal{O}[x]/(x^n)$ where $\mathcal{O}$ is the ring of integers of some number field. We confirm the conjecture for $n\leq 3$ and raise several questions.
Uniform analytic properties of representation zeta functions of finitely generated nilpotent groups
Representation growth of Fuchsian groups and modular forms
Lower Bounds for Representation Growth
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