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$L$-Functions for $\GSp(2)\times \GL(2)$: Archimedean Theory and Applications

  Published:2009-04-01
 Printed: Apr 2009
  • Tomonori Moriyama
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Abstract

Let $\Pi$ be a generic cuspidal automorphic representation of $\GSp(2)$ defined over a totally real algebraic number field $\gfk$ whose archimedean type is either a (limit of) large discrete series representation or a certain principal series representation. Through explicit computation of archimedean local zeta integrals, we prove the functional equation of tensor product $L$-functions $L(s,\Pi \times \sigma)$ for an arbitrary cuspidal automorphic representation $\sigma$ of $\GL(2)$. We also give an application to the spinor $L$-function of $\Pi$.
MSC Classifications: 11F70, 11F41, 11F46 show english descriptions Representation-theoretic methods; automorphic representations over local and global fields
Automorphic forms on ${\rm GL}(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
11F70 - Representation-theoretic methods; automorphic representations over local and global fields
11F41 - Automorphic forms on ${\rm GL}(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
11F46 - Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
 

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