Hyperbolic manifolds and pseudo-arithmeticity

We introduce and motivate a notion of pseudo-arithmeticity, which possibly applies to all lattices in $\mathrm{P}\mathrm{O}(n,1)$ with $n>3$. We further show that under an additional assumption (satisfied in all known cases), the covolumes of these lattices correspond to rational linear combinations of special values of $L$-functions.