Non-vanishing of Jacobi Poincaré series

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

paper · pdf · doi:10.48550/arxiv.0910.4303

15 pages; abstract updated, new results and proofs added

arxiv created 2010/02/01 · arxiv updated 2010/02/08

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.

Related

• Non-vanishing of Hilbert Poincaré series
• On the non-vanishing of Hilbert Poincaré series
• Non-vanishing of Poincaré Series on Average
• Non-vanishing of vector-valued Poincaré series
• Poincaré and Eisenstein series for Jacobi forms of lattice index