Abstract:Let L be a self-adjoint invertible operator in a Hilbert space such that L −1 is p-summable. Under a certain discrete dimension spectrum assumption on L, we study the relation between the (regularized) Fredholm determinant, det p(I+z•L −1 ), on the one hand and the zeta regularized determinant, det ζ (L+z), on the other. One of the main results is the formulaWe show that the derivatives d j dz j log det ζ (L + z)| z=0 can be expressed in terms of (regularized) zeta values and heat trace coefficients of L. Furt… Show more
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