The Hirzebruch-Mumford volume for the orthogonal group and applications

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In this paper we derive an explicit formula for the Hirzebruch-Mumford volume of an indefinite lattice L of rank at least 3. If Γis an arithmetic subgroup of the group O(L) of isometries of L and L has signature (2,n), then an application of Hirzebruch-Mumford proportionality allows us to determine the leading term of the growth of the dimension of the spaces S_k(Γ) of cusp forms of weight k, as k goes to infinity. We compute this in a number of examples, which are important for geometric applications.
Minor corrections, bibliography updated

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Number Theory, Algebraic Geometry, 11F03, 11F23, 14J15, 14J28

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http://salesiana.dossiersoluciones.com/handle/123456789/106401

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0512595
 http://arxiv.org/abs/math/0512595

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arXiv