Given the numbers,
$u\in\mathbb{R}^s$, $\alpha>1$ and $s>1$.
If we have the below Fourier Serie:
$f_{\alpha}(u)=\sum\limits_{h\in\mathbb{Z}^s}\frac{1}{r(h)^{\alpha}}\exp^{2 \pi i \left<h,u\right>}$,
where,
$r(h)=\prod\limits_{i=1}^{s}max(1,\vert h_{i} \vert )$.
Then, the integral of this function over the inside of the hipercube of s dimension has the value of one.
$\int_{[0,1)^{s}}f_{\alpha}(u) du=1$.
I have serious doubts about it. Someone could help me?. Thanks.
Reference: Pricing Options Using Lattice Rules. Phelim P. Boyle, Yongzeng Lai, and Ken Seng Tan.