  It is a well-known fact that Riemann Hypothesis will follows if the function
identically equal to -1 can be arbitrarily approximated in the norm $\norma{.}$
of $L^{2}([0,1],dx)$ by functions of the form $f(x)=\sum_{k=1}^{n}a_{k}
\rho(\frac{\theta_{k}}{x})$, where $\rho(x)\adef\pfrac{x}$, and $a_{k}\in\cc$,
$0<\theta_{k}\leqslant 1$ satisfies $\sum_{k=1}^{n}a_{k} \theta_{k}=0$.
Parsevall Identity $\norma{f(x)+1}^{2}=\sum_{n\in\zz}\modulo{c(n)}^{2}$ is a
possible tool to compute or estimate this norm. In this note we give an
expression for the Fourier coefficients $c(n)$ of $f+1$, when $f$ is a function
defined as above. As an application, we derive an expression for
$M_{f}(s)\adef\int_{0}^{1}(f(x)+1) x^{s-1} dx$ as a series that only depends on
$M_{f}(2k)$, $k\in\nn$. We remark that the Fourier coefficients $c(n)$ depend
on $M_{f}(2k)$ which, for a function $f$ defined as above, can be expressed
also in terms of the $a_{k}$'s and $\theta_{k}$'s. Therefore, a better control
on these parameters will allow to estimate $M_{f}(2k)$ and therefore eventually
to handle $\norma{f+1}$ via our expression for the Fourier coefficients and
Parsevall Identity.
