Abstract
We prove the non-vanishing of a Jacobi Poincaré series for the group \(\varGamma _0(N) \ltimes (\mathbb {Z}^{(g,1)}\times \mathbb {Z}^{(g,1)})\) and matrix index under suitable conditions. In the case when the index is an integer, we improve the conditions of non-vanishing by using the Eichler–Zagier map.
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Acknowledgments
The author would like to thank G.K. Viswanadham for some useful discussions. The author also thanks the referee for his/her meticulous reading of the manuscript and suggesting corrections which improved the manuscript.
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The research of the author was supported by FONDECYT Grant No. 3140554.
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Shankhadhar, K.D. On the non-vanishing of Jacobi Poincaré series. Ramanujan J 43, 1–14 (2017). https://doi.org/10.1007/s11139-016-9826-9
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DOI: https://doi.org/10.1007/s11139-016-9826-9