Minakshisundaram-Pleijel coefficients for non-compact higher rank symmetric spaces

We assign to a non-compact Riemannian symmetric spaceXa theta function and a zeta function. We compute all of the Minakshisundaram-Pleijel coefficients in a short-time asymptotic expansion of the theta function especially whenXis of complex type, which we use to compute the one-loop effective potential-whose relevance for quantum field theory, for example, is briefly commented on. These coefficients, forXof general type, are also shown to be specifically related to residues and special values of the zeta function. The results presented extend previous ones in the literature where the rank ofXis assumed to be one.