We express the ζ-regularized determinant of an elliptic pseudodifferential operator A over S1 with strongly invertible principal symbol in terms of the Fredholm determinant of an operator of determinant class, canonically associated to A, and local invariants. These invariants are given by explicit formulae involving the principal and subprincipal symbol of the operator. We remark that, generically, elliptic pseudodifferential operators have a strongly invertible principal symbol.
- MSC1991: Primary 34L05, Secondary 35S05
ASJC Scopus subject areas
- Algebra and Number Theory