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Chapter
Introduction
Zeta integrals are indispensable tools for studying automorphic representations and their L-functions. In broad terms, it involves integrating automorphic forms (global case) or “coefficients” of representations ...
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Chapter
Analytic Background
Let F be a local field of characteristic zero and G be an affine F-group. Consider a smooth G-variety Y over F, so that Y (F) becomes an F-analytic manifold with right G(F)-action. The constructions below can be ...
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Chapter
Convergence of Some Zeta Integrals
We will need Hypothesis 5.2.2 on the existence of eigenmeasures. This is always met in practice.
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Chapter
The Doubling Method
In order to reconcile our framework with that of Braverman and Kazhdan (Mosc Math J 2:533–553, 2002), two Conjectures 7.1.5 and 7.3.4 will be postulated.
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Chapter and Conference Paper
The Shimura–Waldspurger Correspondence for Mp(2n)
We describe some recent developments and formulate some conjectures in the genuine representation theory and the study of automorphic forms of the metaplectic group Mp(2n), from the point of view of the theta cor...
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Chapter
Towards Generalized Prehomogeneous Zeta Integrals
Let X be a prehomogeneous vector space under a connected reductive group G over ℝ ...
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Chapter
Geometric Background
The main purpose of this section is to fix notation. We refer to Knop (The Luna-Vust theory of spherical embeddings. In: Proceedings of the Hyderabad conference on algebraic groups, Hyderabad, 1989, pp 225–249...
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Chapter
Schwartz Spaces and Zeta Integrals
Throughout this chapter, we fix
a local field F of characteristic zero,
a split connected reductive F-group G,
...