Geodesic
The Hirzebruch-Mumford volume for the orthogonal group and applications
Documenta mathematica, Tome 12 (2007), pp. 215-241
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In this paper we derive an explicit formula for the Hirzebruch-Mumford volume of an indefinite lattice L of rank ≥3. If Γ⊂O(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 Sk​(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.
DOI : 10.4171/dm/224
Classification : 11F55, 14G35, 32N15 
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G.K. Sankaran; V. Gritsenko; K. Hulek. The Hirzebruch-Mumford volume for the orthogonal group and applications. Documenta mathematica, Tome 12 (2007), pp. 215-241. doi: 10.4171/dm/224

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