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NONVANISHING OF JACOBI POINCARÉ SERIES

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  12 January 2011

SOUMYA DAS
SOUMYA DAS*
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400005, India (email: [email protected])
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Abstract

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We prove that, under suitable conditions, a Jacobi Poincaré series of exponential type of integer weight and matrix index does not vanish identically. For the classical Jacobi forms, we construct a basis consisting of the ‘first’ few Poincaré series, and also give conditions, both dependent on and independent of the weight, that ensure the nonvanishing of a classical Jacobi Poincaré series. We also obtain a result on the nonvanishing of a Jacobi Poincaré series when an odd prime divides the index.

Keywords

Jacobi formsPoincaré seriesKloosterman sums

MSC classification

Secondary: 11F50: Jacobi forms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 2 , October 2010 , pp. 165 - 179
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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