  In our last work, we formulate a Fourier transformation on the
infinite-dimensional space of functionals. Here we first calculate the Fourier
transformation of infinite-dimensional Gaussian distribution $\exp(-\pi
\xi\int_{-\infty}^{\infty}\alpha ^2(t)dt)$ for $\xi\in{\bf C}$ with
Re$(\xi)>0$, $\alpha \in L^2({\bf R})$, using our formulated Feynman path
integral. Secondly we develop the Poisson summation formula for the space of
functionals, and define a functional $Z_s$, $s\in {\bf C}$, the Feynman path
integral of that corresponds to the Riemann zeta function in the case
Re$(s)>1$.
