Whittaker Coefficients of Metaplectic Eisenstein Series
نویسندگان
چکیده
منابع مشابه
Whittaker Coefficients of Metaplectic Eisenstein Series
We study Whittaker coefficients for maximal parabolic Eisenstein series on metaplectic covers of split reductive groups. By the theory of Eisenstein series these coefficients have meromorphic continuation and functional equation. However they are not Eulerian and the standard methods to compute them in the reductive case do not apply to covers. For “cominuscule” maximal parabolics, we give an e...
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1.1. Steve Gelbart, Whittaker models and the metaplectic group. The metaplectic double cover of Sp(2r) and the Weil representation were introduced by Weil [37] in order to formulate results of Siegel on theta functions in the adelic setting. This was followed by two initially independent developments. First, Shimura [32], [33] gave two extremely important constructions involving modular forms o...
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Let F be a global field with ring o of integers, and let μn denote the group of n-th roots of unity in F . Let Γ(f) be the principal congruence subgroup of SL3(o) consisting of elements that are congruent to the identity modulo f. The Kubota symbol κ : Γ(f) −→ μn is a character constructed by Bass, Milnor and Serre [1]. We will give a direct construction, obtaining on the way new formulas for t...
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The theory of Whittaker functions is of crucial importance in the classical study of automorphic forms on adele groups. Motivated by the appearance of Whittaker functions for covers of reductive groups in the theory of multiple Dirichlet series, we provide a study of Whittaker functions on metaplectic covers of reductive groups over local fields. Thesis Supervisor: Benjamin Brubaker Title: Assi...
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Let A be the adeles of the function eld Fq (T). If E(g; s) is the Eisenstein series associated with the spherical vector in the principal series representation of the double cover of GL2(A), then the Fourier coeecients (Whittaker functions) of E(g; s) have an Euler product and satisfy a `Riemann Hypothesis' condition. Namely, the zeros occur only on the line <(s) = 0. These Whittaker functions ...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2015
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-015-0329-4