scholarly journals Regularized periods of automorphic forms on $GL(2)$

2013 ◽  
Vol 65 (3) ◽  
pp. 373-409 ◽  
Author(s):  
Shingo Sugiyama
Keyword(s):  
Automorphic Forms ◽  
Periods Of Automorphic Forms

scholarly journals Periods of automorphic forms: the case of

2014 ◽  
Vol 151 (4) ◽  
pp. 665-712 ◽  
Author(s):  
Atsushi Ichino ◽  
Shunsuke Yamana
Keyword(s):  
Automorphic Form ◽  
Automorphic Forms ◽  
Selberg Integral ◽  
Selberg Integrals ◽  
Diagonal Subgroup ◽  
Periods Of Automorphic Forms

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 $\text{GL}_{n+1}\times \text{GL}_{n}$.

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