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L-Functions for GSp(2) × GL(2): Archimedean Theory and Applications

Published online by Cambridge University Press:  20 November 2018

Tomonori Moriyama
Tomonori Moriyama*
Affiliation:
Department of Mathematics, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka, 560-0043, Japan, moriyama@math.sci.osaka-u.ac.jp
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Abstract

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Let $\Pi$ be a generic cuspidal automorphic representation of $\text{GSp}\left( 2 \right)$ defined over a totally real algebraic number field $\text{k}$ 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 $L\left( s,\Pi \times \sigma \right)$ for an arbitrary cuspidal automorphic representation $\sigma $ of $\text{GL}\left( 2 \right)$. We also give an application to the spinor $L$-function of $\Pi$.

Keywords

11F7011F4111F46
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 2 , 01 April 2009 , pp. 395 - 426
Copyright
Copyright © Canadian Mathematical Society 2009

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