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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
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References:

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