Spectral invariants of the magnetic Dirichlet-to-Neumann map on Riemannian manifolds

This paper is devoted to investigating the heat trace asymptotic expansion associated with the magnetic Steklov problem on a smooth compact Riemannian manifold (Omega, g) with smooth boundary partial derivative Omega. By computing the full symbol of the magnetic Dirichlet-to-Neumann map M, we establish an effective procedure, by which we can calculate all the coefficients a(0), a(1), ..., a(n-1) of the asymptotic expansion. In particular, we explicitly give the first four coefficients a(0), a(1), a(2), and a(3). They are spectral invariants, which provide precise information concerning the volume and curvatures of the boundary partial derivative Omega and some physical quantities.