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We extend the spectral theory of generalized Laplacians to integrable metricson compact Riemann surfaces. As a consequence, we attach in a direct way, aholomorphic analytic torsion to any integrable metrics. We also provide adifferent approach to define the holomorphic analytic torsion. We prove thatboth approaches agree.

The spectral theory of generalized Laplacians associated to integrable metrics on compact Riemann surfaces