ZETA-FUNCTIONS FOR NONMINIMAL OPERATORS

We evaluate zeta functions zeta(s) at s = 0 for invariant nonminimal second-order vector and tenser operators defined on maximally symmetric even dimensional spaces. We decompose the operators into their irreducible parts and obtain their corresponding eigenvalues. Using these eigenvalues, we are able to explicitly calculate zeta(0) for the cases of Euclidean spaces and N-spheres. In the N-sphere case, we make use of the Euler-Maclaurin formula to develop asymptotic expansions for the required sums. The resulting zeta(0) values for dimensions 2 to 10 are given in the Appendix.