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PERIODS OF AUTOMORPHIC FORMS: THE TRILINEAR CASE
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 17 / Issue 1 / February 2018
- Published online by Cambridge University Press:
- 26 October 2015, pp. 59-74
- Print publication:
- February 2018
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Endoscopie et conjecture locale raffinée de Gan–Gross–Prasad pour les groupes unitaires
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- Journal:
- Compositio Mathematica / Volume 151 / Issue 7 / July 2015
- Published online by Cambridge University Press:
- 18 February 2015, pp. 1309-1371
- Print publication:
- July 2015
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Under endoscopic assumptions about
$L$-packets of unitary groups, we prove the local Gan–Gross–Prasad conjecture for tempered representations of unitary groups over 
$p$-adic fields. Roughly, this conjecture says that branching laws for 
$U(n-1)\subset U(n)$ can be computed using epsilon factors.
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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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 
$\text{GL}_{n+1}\times \text{GL}_{n}$.
