I just learnt that a $ d $-regular graph $ G $ is a Ramanujan graph if $\lambda(G)\leq 2\sqrt{d-1} $, and that this condition is equivalent to the Ihara zeta function fulfilling the analog of RH.
But the condition defining a Ramanujan graph is formally analogous to the Ramanujan conjecture $ \tau(p)\leq 2\sqrt{p^{k-1}} $ with $ k=12 $ the weight of the cusp form whose Fourier coefficients are the $\tau(n) $ in a " $ \log p $ free" form.
So can an L-function fulfilling both the Ramanujan conjecture and RH be viewed as the Ihara zeta function of some $ d $ -regular graph with $ d $ depending in a way to be precised on the considered L-function ? As the definition of a Ramanujan graph is independent of any prime number, is it actually some kind of archimedean Ramanujan conjecture ?