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Betti numbers of Shimura curves and arithmetic three--orbifolds
Published 24 Oct 2018 in math.DG and math.NT | (1810.10515v1)
Abstract: We show that asymptotically the first Betti number, or the arithmetic genus, of a Shimura curve satisfies the Gauss--Bonnet equality. We also show that the first Betti number of a congruence hyperbolic 3--orbifold asymptotically vanishes relatively to hyperbolic volume.
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