Complex powers of hypoelliptic systems in $\mathbf R^n$

A system of differential operators in $\mathbf R^n$ with polynomial coefficients and whose symbol is hypoelliptic in $(x;\xi)$ is considered. The complex powers and the zeta-function of such a system are constructed. A meromorphic extension of the zeta-function is obtained, from which there follows an asymptotic result concerning the spectrum of the system. The results of Hironaka on the resolution of singularities are used in the proofs.
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