Non-vanishing of Jacobi Poincar\'{e} series
Number Theory
2010-02-01 v2
Abstract
We prove that under suitable conditions, the Jacobi Poincar\'{e} series of exponential type of integer weight and matrix index does not vanish identically. For classical Jacobi forms, we construct a basis consisting of the "first" few Poincar\'{e} series and also give conditions both dependent and independent of the weight, which ensures non-vanishing of classical Jacobi Poincar\'{e} series. Equality of certain Kloosterman-type sums is proved. Also, a result on the non-vanishing of Jacobi Poincar\'{e} series is obtained when an odd prime divides the index.
Cite
@article{arxiv.0910.4303,
title = {Non-vanishing of Jacobi Poincar\'{e} series},
author = {Soumya Das},
journal= {arXiv preprint arXiv:0910.4303},
year = {2010}
}
Comments
15 pages; abstract updated, new results and proofs added