Automorphic products of singular weight for simple lattices

Abstract

We classify the simple even lattices of square free level and signature (2,n) for n > 3. A lattice is called simple if the space of cusp forms of weight 1+n/2 for the dual Weil representation of the lattice is trivial. For a simple lattice every formal principal part obeying obvious conditions is the principal part of a vector valued modular form. Using this, we determine all holomorphic Borcherds products of singular weight (arising from vector valued modular forms with non-negative principal part) for the simple lattices. We construct the corresponding vector valued modular forms by eta products and compute expansions of the automorphic products at different cusps.

arXiv comment22 pages

References in corpus (1)

• Automorphic forms with singularities on Grassmannians

Cited by in corpus (7)

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• Poincaré square series for the Weil representation
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• Holomorphic Borcherds products of singular weight for simple lattices of arbitrary level
• Consistency of eight-dimensional supergravities: Anomalies, Lattices and Counterterms
• Orthogonal Eisenstein Series at Harmonic Points and Modular Forms of Singular Weight