I took a quick glance on a survey paper about superzeta functions where one considers a pair $\rho\leftrightarrow 1-\rho$ of non trivial zeroes of the Riemann zeta function. The assumption of RH, i.e $\rho=1/2+it\_{k}$ yields $\rho(1-\rho)=1/4+t\_{k}^{2}$. Hence my question: can the eigenvalues considered in Selberg eigenvalue conjecture be interpreted as products of this form?
Many thanks in advance.



Is Selberg's eigenvalue conjecture related to RH?
Selberg's 1/4 conjecture can be phrased like this: For a congruence subgroup all non-trivial zeros of the Selberg zeta function either come from resonances, which means that they lie at $\mathrm{Re}(s) < 1/2\ $ or they come from eigenvalues and lie at $\mathrm{Re}(s)= 1/2\ $.


