  The Riemann Hypothesis states that the Riemann zeta function $\zeta(z)$
admits a set of ``non-trivial'' zeros that are complex numbers supposed to have
real part $1/2$. Their distribution on the complex plane is thought to be the
key to determine the number of prime numbers before a given number. Hilbert and
P\'olya suggested that the Riemann Hypothesis could be solved through the
mathematical tools of physics, finding a suitable Hermitian or unitary operator
that describe classical or quantum systems, whose eigenvalues distribute like
the zeros of $\zeta(z)$. A different approach is that of finding a
correspondence between the distribution of the $\zeta(z)$ zeros and the poles
of the scattering matrix $S$ of a physical system. Our contribution is
articulated in two parts: in the first we apply the infinite-components
Majorana equation in a Rindler spacetime and compare the results with those
obtained with a Dirac particle following the Hilbert-P\'olya approach showing
that the Majorana solution has a behavior similar to that of massless Dirac
particles and finding a relationship between the zeros of zeta end the energy
states. Then, we focus on the $S$-matrix approach describing the bosonic open
string scattering for tachyonic states with the Majorana equation. Here we find
that, thanks to the relationship between the angular momentum and energy/mass
eigenvalues of the Majorana solution, one can explain the still unclear point
for which the poles and zeros of the $S$-matrix of an ideal system that can
satisfy the Riemann Hypothesis, exist always in pairs and are related via
complex conjugation. As claimed in the literature, if this occurs and the claim
is correct, then the Riemann Hypothesis could be in principle satisfied,
tracing a route to a proof.
