Determinants of Zeroth Order Operators

@inproceedings{Guillemin2006DeterminantsOZ,
  title={Determinants of Zeroth Order Operators},
  author={Victor Guillemin},
  year={2006}
}
For compact Riemannian manifolds all of whose geodesics are closed (aka Zoll manifolds) one can define the determinant of a zeroth order pseudodifferential operator by mimicking Szego’s definition of this determinant for the operator: multiplication by a bounded function, on the Hilbert space of square-integrable functions on the circle. In this paper we prove that the non-local contribution to this determinant can be computed in terms of a much simpler “zeta-regularized” determinant. 

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