Towards a Pólya-Carlson dichotomy for algebraic dynamics (Q2252938)

The article considers the Pólya-Carlson Theorem for power series and suggests that a similar result might be true for group automorphisms. The conjecture states that the zeta function of a compact group automorphism is either rational or admits a natural boundary at its radius of convergence. The article does not prove it in fully generality, but shows it for a large class of automorphisms of connected finite-dimensional abelian groups (so called solenoid). In addition the authors give some arguments explaining why they think that the conjecture is plausible and what issues would arise in attempting to prove it.