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Periods of automorphic forms: the case of $(\text{GL}_{n+1}\times \text{GL}_{n},\text{GL}_{n})$

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  13 November 2014

Atsushi Ichino  and
Shunsuke Yamana
Atsushi Ichino
Affiliation:
Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan email ichino@math.kyoto-u.ac.jp
Shunsuke Yamana
Affiliation:
Faculty of Mathematics, Kyushu University, Motooka, Nishi-ku, Fukuoka 819-0395, Japan email yamana@math.kyushu-u.ac.jp
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Abstract

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Following Jacquet, Lapid and Rogawski, we define a regularized period of an automorphic form on $\text{GL}_{n+1}\times \text{GL}_{n}$ along the diagonal subgroup $\text{GL}_{n}$ and express it in terms of the Rankin–Selberg integral of Jacquet, Piatetski-Shapiro and Shalika. This extends the theory of Rankin–Selberg integrals to all automorphic forms on $\text{GL}_{n+1}\times \text{GL}_{n}$.

Keywords

tensor product L-functionsWhittaker functionsGan–Gross–Prasad conjecture

MSC classification

Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 4 , April 2015 , pp. 665 - 712
Copyright
© The Author(s) 2014 

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