On local Whittaker models for the Jacobi group of degree one
Tóm tắt
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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