We give an explicit formula for certain global trilinear forms that appear in Jacquet's conjecture in terms of local trilinear forms and the central values of triple product $L$-functions
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References
S. BöCherer and R. Schulze-Pillot, ``On the central critical value of the triple product $L$-function'' in Number Theory (Paris, 1993--1994.), London Math. Soc. Lecture Note Ser. 235, Cambridge Univ. Press, Cambridge, 1996, 1--46.
P. B. Garrett, Decomposition of Eisenstein series: Rankin triple products, Ann. of Math. (2) 125 (1987), 209--235.
B. H. Gross and S. S. Kudla, Heights and the central critical values of triple product $L$-functions, Compositio Math. 81 (1992), 143--209.
B. H. Gross and D. Prasad, On the decomposition of a representation of $\mathrmSO_n$ when restricted to $\mathrmSO_n-1$, Canad. J. Math. 44 (1992), 974--1002.
M. Harris and S. S. Kudla, The central critical value of a triple product $L$-function, Ann. of Math. (2) 133 (1991), 605--672.
—, ``On a conjecture of Jacquet'' in Contributions to Automorphic Forms, Geometry, and Number Theory (Baltimore, 2002), Johns Hopkins Univ. Press, Baltimore, 2004, 355--371.
K. Hiraga and H. Saito, On $L$-packets for inner forms of $\mathrmSL_n$, preprint, 2007.
A. Ichino and T. Ikeda, On the periods of automorphic forms on special orthogonal groups and the Gross-Prasad conjecture, preprint, 2007.
T. Ikeda, On the location of poles of the triple $L$-functions, Compositio Math. 83 (1992), 187--237.
H. H. Kim and F. Shahidi, Functorial products for $\mathrmGL_2 \times \mathrmGL_3$ and the symmetric cube for $\mathrmGL_2$, Ann. of Math. (2) 155 (2002), 837--893.
S. S. Kudla and S. Rallis, A regularized Siegel-Weil formula: The first term identity, Ann. of Math. (2) 140 (1994), 1--80.
H. Y. Loke, Trilinear forms of $\mathfrakgl_2$, Pacific J. Math. 197 (2001), 119--144.
I. Piatetski-Shapiro and S. Rallis, Rankin triple $L$ functions, Compositio Math. 64 (1987), 31--115.
D. Prasad, Trilinear forms for representations of $\mathrmGL(2)$ and local $\epsilon$-factors, Compositio Math. 75 (1990), 1--46.
—, Invariant forms for representations of $\mathrmGL_2$ over a local field, Amer. J. Math. 114 (1992), 1317--1363.
D. Prasad and R. Schulze-Pillot, Generalised form of a conjecture of Jacquet and a local consequence, J. Reine Angew. Math. 616 (2008), 219--236.
H. Shimizu, Theta series and automorphic forms on $\mathrmGL_2$, J. Math. Soc. Japan 24 (1972), 638--683.
Mathematical Reviews (MathSciNet):
MR033081
J.-L. Waldspurger, Sur les valeurs de certaines fonctions $L$ automorphes en leur centre de symétrie, Compositio Math. 54 (1985), 173--242.
T. C. Watson, Rankin triple products and quantum chaos, to appear in Ann. of Math. (2), Ph.D. dissertation, Princeton University, Princeton, 2002.
A. Weil, Sur certains groupes d'opérateurs unitaires, Acta Math. 111 (1964), 143--211.