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arXiv · 0910.4303

Non-vanishing of Jacobi Poincaré series

Soumya Das
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Abstract

We prove that under suitable conditions, the Jacobi Poincaré 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 Poincaré series and also give conditions both dependent and independent of the weight, which ensures non-vanishing of classical Jacobi Poincaré series. Equality of certain Kloosterman-type sums is proved. Also, a result on the non-vanishing of Jacobi Poincaré series is obtained when an odd prime divides the index.

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Soumya Das. 2010-02-01. Non-vanishing of Jacobi Poincaré series. https://arxiv.org/abs/0910.4303

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