Heat Determinant on Manifolds
  We introduce and study new invariants associated with Laplace type elliptic partial differential operators on manifolds. These invariants are constructed by using the off-diagonal heat kernel; they are not pure spectral invariants, that is, they depend not only on the eigenvalues but also on the corresponding eigenfunctions in a non-trivial way. We compute the first three low-order invariants explicitly. 
Ivan G. Avramidi and Benjamin J. Buckman
math-ph math.DG math.MP