Even unimodular Lorentzian lattices and hyperbolic volume
Abstract.
We compute the hyperbolic covolume of the automorphism group of each even unimodular Lorentzian lattice. The result is obtained as a consequence of a previous work with Belolipetsky, which uses Prasad's volume to compute the volumes of the smallest hyperbolic arithmetic orbifolds.
I would like to thank Curtis McMullen for the interesting discussions that are at the origin of this article. I thank Jiu-Kang Yu for his help concerning Bruhat–Tits theory, Steve Tschantz for the numerical computation mentioned in Section 3, Anna Felikson and Pavel Tumarkin for helpful discussions, and Ruth Kellerhals, John Ratcliffe and the referee for helpful comments. I am thankful to the MPIM in Bonn for the hospitality and the financial support.
© 2014 by Walter de Gruyter Berlin/Boston
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- UC hierarchy and monodromy preserving deformation
- Vector-valued p-adic Siegel modular forms
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- Errata to Algebraic points on Shimura curves of Γ0(p)-type (J. reine angew. Math., DOI 10.1515/crelle-2012-0068)
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Articles in the same Issue
- Frontmatter
- UC hierarchy and monodromy preserving deformation
- Vector-valued p-adic Siegel modular forms
- K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux
-
Strichartz estimates for partially periodic solutions to Schrödinger equations in
- Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line
- Mean curvature flow of entire graphs in a half-space with a free boundary
- Ricci flow and the holonomy group
- Uniqueness of compact tangent flows in Mean Curvature Flow
- Even unimodular Lorentzian lattices and hyperbolic volume
- Algebraic points on Shimura curves of Γ0(p)-type
- Errata to Algebraic points on Shimura curves of Γ0(p)-type (J. reine angew. Math., DOI 10.1515/crelle-2012-0068)
- Property A and the operator norm localization property for discrete metric spaces
- Stable manifolds for holomorphic automorphisms
