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

2023/10/25 by Shaul Zemel, Zemel, Shaul · 1 citation
Chemistry · Mathematics · #11F27 #11F37 #11F50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2310.16508

openalex publication_date 2023/10/25 · openalex created_date 2023/10/27 · openalex updated_date 2026/07/28

Abstract

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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• The cohomological Kudla conjecture for unitary Shimura varieties

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