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Determinants of zeroth order operators. (English) Zbl 1140.58017
Summary: 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.

58J52 Determinants and determinant bundles, analytic torsion
58J40 Pseudodifferential and Fourier integral operators on manifolds
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