2022
DOI: 10.48550/arxiv.2204.08262
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Taylor expansions of Jacobi forms and linear relations among theta series

Abstract: We study Taylor expansions of Jacobi forms of lattice index. As the main result, we give an embedding from certain space of such forms, whether scalar-valued or vector-valued, integral-weight or half-integral-weight, of any level, with any character, into a product of finitely many spaces of modular forms. As an application, we investigate linear relations among Jacobi theta series of lattice index. Many linear relations among the second powers of such theta series associated with the D 4 lattice and A 3 latti… Show more

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