Automorphic L-functions of half-integral weight

Stephen Gelbart, Ilya Piatetski-Shapiro

Type: Article

Publication Date: 1978-04-01

Citations: 7

DOI: https://doi.org/10.1073/pnas.75.4.1620

Abstract

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.

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Works That Cite This (7)

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+	Uniqueness of Whittaker-models for irreducible objects in Alg(Mp(k))	1987	G.F. Helminck
+ PDF Chat	On Supercuspidal Representations of the Metaplectic Group	1981	James Meister
+	Uniqueness and existence of Whittaker models for the metaplictic group	1979	Stephen Gelbart Roger Howe Ilya Piatetski-Shapiro
+	On Shimura’s Correspondence for Modular Forms of Half-Integral Weight	1981	Stephen Gelbart Ilya Piatetski-Shapiro
+	A converse theorem for metaplectic Eisenstein series on the double and triple covers of SL2(ℚ(−D))	2015	Vladislav Petkov
+	Modular forms	1983	A. A. Panchishkin
+ PDF Chat	On supercuspidal representations of the metaplectic group	1981	James Meister

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