2 00 1 Integrals of Borcherds forms by
نویسنده
چکیده
Let V be a non-degenerate inner product space over Q of signature (n, 2), and let D be the space of oriented negative 2-planes in V (R). In [2], Borcherds constructed certain meromorphic modular forms Ψ(F ) on D with respect to arithmetic subgroups ΓM of G = O(V ) by regularizing the theta integral of vector valued elliptic modular forms f of weight 1 − n 2 for SL2(Z) with poles at the cusp, cf. also [1], [21], [7], [8]. The Borcherds forms Ψ(f) can be viewed as meromorphic sections of powers of a certain line bundle L on X = ΓM\D. Taking the standard Petersson metric || || on L, it is of interest in Arakelov geometry to compute the integral:
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