Abstract
We give a characterisation of Jacobi forms by classical modular forms from which we obtain dimension formulas for the spaces of Jacobi forms in certain cases. Then we consider the ordinary theta series to the quaternary quadratic forms of discriminant q2 (q an odd prime) representing 2; these possess a ‘natural’ continuation to Jacobi forms for which we give a sufficient condition of linear independence. If this condition is fulfilled and if there is no cusp form of weight 4 with respect to Γo(q) which vanishes at the cusp 0 with a certain order then the classical theta series are also linear independent.
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Kramer, J. Jacobiformen und Thetareihen. Manuscripta Math 54, 279–322 (1986). https://doi.org/10.1007/BF01171338
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DOI: https://doi.org/10.1007/BF01171338