A string algebra is domestic if and only if its μ-series is rational, via a zeta-function analogue of the prime number theorem.
Auslander-reiten sequences with few middle terms and applications to string algebras
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On Zeta functions and $\mu$-series of string algebras
A string algebra is domestic if and only if its μ-series is rational, via a zeta-function analogue of the prime number theorem.