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arXiv · 1502.02466

Automorphic products of singular weight for simple lattices

Moritz Dittmann·Heike Hagemeier·Markus Schwagenscheidt
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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.

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Moritz Dittmann, Heike Hagemeier, Markus Schwagenscheidt. 2015-02-09. Automorphic products of singular weight for simple lattices. https://doi.org/10.1007/s00209-014-1383-6

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