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$L$-Functions for $\GSp(2)\times \GL(2)$: Archimedean Theory and Applications |
Canad. J. Math. 61(2009), 395-426
Published:2009-04-01
Printed: Apr 2009
Printed: Apr 2009
- Tomonori Moriyama
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 - 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 |