2021
DOI: 10.1090/btran/48
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Hyperbolic manifolds and pseudo-arithmeticity

Abstract: We introduce and motivate a notion of pseudo-arithmeticity, which possibly applies to all lattices in PO ⁡ ( n , 1 ) \operatorname {PO}(n,1) with n > 3 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 L -functions.

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Cited by 3 publications
(9 citation statements)
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“…Therefore M / ∈ A gl . However, it turns out that this manifold M is still pseudo-arithmetic (see [EM18] and Chapter 5).…”
Section: Arithmetic Piecesmentioning
confidence: 99%
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“…Therefore M / ∈ A gl . However, it turns out that this manifold M is still pseudo-arithmetic (see [EM18] and Chapter 5).…”
Section: Arithmetic Piecesmentioning
confidence: 99%
“…The goal of this final chapter is to present the notion of pseudo-arithmeticity and motivate it using the trace field computations from the previous sections. The content of this chapter is a more detailed version of a joint work with Vincent Emery [EM18]. In the first section, we start by introducing pseudoarithmetic manifolds and deduce from the results established in the previous chapters that all gluings of arithmetic pieces are pseudo-arithmetic.…”
Section: Chapter 5 | Pseudo-arithmeticity and Volumesmentioning
confidence: 99%
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