Automorphic L-functions of half-integral weight.
We describe a theory of Whittaker models and L-functions for irreducible representations of a metaplectic covering group of GL(2). We explain how to use these L-functions to establish an arithmetical correspondence between "genuine" cuspidal representations of the metaplectic group and cuspidal representations of GL(2). When our ground field is Q, this correspondence generalizes and reformulates recent results of G. Shimura [(1973) Ann. Math. 97, 440-481]. A crucial role in our theory is played by what we call "exceptional" cusp forms-those that are completely determined by just one Fourier coefficient.
Department of Mathematics, Cornell University, Ithaca, New York 14853.
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Gelbart
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Piatetski-Shapiro