Note on Hermitian Jacobi Forms

Soumya Das

Note on Hermitian Jacobi Forms

Number Theory 2010-02-02 v2

Authors: Soumya Das

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.

Keywords

jacobi forms jacobian conjecture modular forms

Cite

@article{arxiv.0910.4312,
  title  = {Note on Hermitian Jacobi Forms},
  author = {Soumya Das},
  journal= {arXiv preprint arXiv:0910.4312},
  year   = {2010}
}

Comments

24 pages; title changed, abstract changed, some proofs expanded and new results added

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