Geodesic
The Hirzebruch-Mumford volume for the orthogonal group and applications
Documenta mathematica, Tome 12 (2007), pp. 215-241.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we derive an explicit formula for the Hirzebruch-Mumford volume of an indefinite lattice $L$ of rank $\ge 3$. If $\Gamma \subset \Orth(L)$ is an arithmetic subgroup 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 $S_k(\Gamma)$ 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.
Classification : 11F55, 32N15, 14G35 
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     title = {The {Hirzebruch-Mumford} volume for the orthogonal group and applications},
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Gritsenko, V.; Hulek, K.; Sankaran, G.K. The Hirzebruch-Mumford volume for the orthogonal group and applications. Documenta mathematica, Tome 12 (2007), pp. 215-241. http://geodesic.mathdoc.fr/item/DOCMA_2007__12__a14/