Hermitian Jacobi Forms Having Modules as their Index and Vector-Valued Jacobi Forms
Number Theory
2023-10-26 v1
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.
Keywords
Cite
@article{arxiv.2310.16508,
title = {Hermitian Jacobi Forms Having Modules as their Index and Vector-Valued Jacobi Forms},
author = {Shaul Zemel},
journal= {arXiv preprint arXiv:2310.16508},
year = {2023}
}
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60 pages