## Hyperbolic manifolds and pseudo-arithmeticity.(English)Zbl 07346764

Summary: We introduce and motivate a notion of pseudo-arithmeticity, which possibly applies to all lattices in $$\operatorname{PO}(n,1)$$ 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.

### MSC:

 22E40 Discrete subgroups of Lie groups 20G30 Linear algebraic groups over global fields and their integers 51M25 Length, area and volume in real or complex geometry

### Software:

SageMath; CoxIter
Full Text:

### References:

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