Note on Hermitian Jacobi Forms

2009/10/22 by Das, Soumya
#11F50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0910.4312

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. 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.

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