  In this note, we prove in full generality a conjecture of Jacquet concerning
the nonvanishing of the triple product L-function at the central point.
  Let $\kay$ be a number field and let $\pi_i$, $i=1$, 2, 3 be cuspidal
automorphic representations of $GL_2(\A)$ such that the product of their
central characters is trivial. Then the central value
$L(\frac12,\pi_1\otimes\pi_2\otimes\pi_3)$ of the triple product L--function is
nonzero if and only if there exists a quaternion algebra $B$ over $\kay$ and
automorphic forms $f_i^B\in \pi_i^B$, such that the integral of the product
$f_1^B f_2^B f_3^B$ over the diagonal $Z(\Bbb A) B^\times(\kay) B^\times(\Bbb
A)$ is nonzero, where $\pi_i^B$ is the representation of $B^\times(\A)$
corresponding to $\pi_i$.
  In a previous paper, we proved this conjecture in the special case where
$\kay=\Q$ and the $\pi_i$'s correspond to a triple of holomorphic newforms.
Recent improvement on the Ramanujan bound due to Kim and Shahidi, results about
the local L-factors due to Ikeda and Ramakrishnan, results of Chen-bo Zhu and
Sahi about invariant distributions and degenerate principal series in the
complex case, and an extension of the Siegel--Weil formula to similitude groups
allow us to carry over our method to the general case.
