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Periods of automorphic forms: the case of
$(\text{GL}_{n+1}\times \text{GL}_{n},\text{GL}_{n})$
- Part of
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- Journal:
- Compositio Mathematica / Volume 151 / Issue 4 / April 2015
- Published online by Cambridge University Press:
- 13 November 2014, pp. 665-712
- Print publication:
- April 2015
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- Article
- Export citation
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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 
$\text{GL}_{n+1}\times \text{GL}_{n}$.
