## Global Theta Liftings of General Linear Groups

J. Math. Sci. Univ. Tokyo
Vol. 3 (1996), No. 3, Page 699--711.

Watanabe, Takao
Global Theta Liftings of General Linear Groups
A global theta lifting of some irreducible type 2 dual reductive pair is studied. It is proved that the image of a global theta lifting of a given irreducible automorphic cuspidal representation is nonvanishing if and only if its standard $L$-function is nonzero at the point $1/2$, and then the image coincides with the initial automorphic cuspidal representation. As a corollary of this result, the global Howe correspondence is obtained.