Note on Hermitian Jacobi forms

Soumya Das

doi:10.21099/tkbjm/1283967408

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Home > Journals > Tsukuba J. Math. > Volume 34 > Issue 1 > Article

August 2010 Note on Hermitian Jacobi forms

Soumya Das

Tsukuba J. Math. 34(1): 59-78 (August 2010). DOI: 10.21099/tkbjm/1283967408

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Abstract

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. Upper bounds for the order of vanishing of HJF at the origin are 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.