  We study the algebraic structure of the eigenvalues of a Hamiltonian that
corresponds to a many-body fermionic system. As the Hamiltonian is quadratic in
fermion creation and/or annihilation operators, the system is exactly
integrable and the complete single fermion excitation energy spectrum is
constructed using the non-interacting fermions that are eigenstates of the
quadratic matrix related to the system Hamiltonian. Connection to the Riemann
Hypothesis is discussed.
