Soumya Das
Published 2009-10-22, updated 2010-02-02Version 2
We compare the spaces of Hermitian Jacobi forms (HJF) of weight $k$ and indices $1,2$ with classical Jacobi forms (JF) of weight $k$ and indices $1,2,4$. Using the embedding into JF, upper bounds for the order of vanishing of HJF at the origin is obtained. We compute the rank of HJF as a module over elliptic modular forms and prove the algebraic independence of the generators in case of index 1. Some related questions are discussed.
Comments: 24 pages; title changed, abstract changed, some proofs expanded and new results added
Hermitian Jacobi Forms Having Modules as their Index and Vector-Valued Jacobi Forms
Lifting from pairs of two elliptic modular forms to Siegel modular forms of half-integral weight of even degree
Algebraic Independence and Mahler's method
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