Abstract
The lowest dimensional Jacobi groupG J sets a link between the theory of Siegel modular forms of degree two and the elliptic modular forms of integral and half integral weight. This note is meant to help finding a way to associateL-functions to automorphic representations of the groupG J by using the approach via Whittaker models of these representations. Thus, here the question of existence and unicity of these models is discussed. This question may be reduced to a closer study of the Schrödinger and Weil representation of the Heisenberg resp. the metaplectic group and thus to the application of some results by Waldspurger.
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Berndt, R. On local Whittaker models for the Jacobi group of degree one. Manuscripta Math 84, 177–191 (1994). https://doi.org/10.1007/BF02567452
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DOI: https://doi.org/10.1007/BF02567452