Counterexamples to the ordinary Fried conjecture near hyperbolic metrics

Abstract

We give an LLM-assisted construction of counterexamples to the ordinary Fried conjecture, with real analytic metrics arbitrarily close to a hyperbolic metric in dimension three. For acyclic unitary line characters tending to the trivial character, the modulus of the Ruelle zeta function at zero divided by analytic torsion squared tends to zero.