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Hermitian Jacobi Forms Having Modules as their Index and Vector-Valued Jacobi Forms

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arxiv 2310.16508 v1 pith:POZC3SR6 submitted 2023-10-25 math.NT

Shaul Zemel This is my paper · ORCID
classification math.NT
keywords formshermitianjacobiindexmatrixorthogonalvector-valuedallows
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We develop the theory of Hermitian Jacobi forms of lattice index, for both definite and indefinite Hermitian lattices. We also prove a theta decomposition theorem for vector-valued Jacobi forms (both in the orthogonal and Hermitian settings), with enhanced periodicity properties. This allows us to give a good definition of orthogonal and Hermitian Jacobi forms of matrix index, when the matrix need not be integral in any natural sense.

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  1. The cohomological Kudla conjecture for unitary Shimura varieties

    math.NT 2025-07 conditional novelty 8.0 of 10

    The authors construct explicit boundary corrections making the Kudla-Millson generating series of special cycles on compactified unitary Shimura varieties a holomorphic Hermitian modular form for codimensions g ≤ n/2.

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