A new converse theorem for Borcherds products
Ingmar Metzler
TL;DR
This paper introduces a new converse theorem for Borcherds products and proves the injectivity of the Kudla-Millson theta lift in a broader setting for O(n,2) lattices, under specific lattice assumptions.
Contribution
It presents a novel converse theorem for Borcherds products and extends the injectivity results of the Kudla-Millson theta lift to more general O(n,2) cases.
Findings
New converse theorem for Borcherds products established
Injectivity of Kudla-Millson theta lift demonstrated in broader cases
Results depend on a single hyperbolic split of the lattice
Abstract
We establish a new converse theorem for Borcherds products. Moreover, the injectivity of the Kudla-Millson theta lift is demonstrated in the O case in greater generality than is currently available in the literature. Both results are derived under the assumption of a single hyperbolic split of the base lattice.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Operator Algebra Research · Random Matrices and Applications