Liftings of automorphic representations and L-functions

我给出了升降不消失的充分必要条件。构造了自同构形式的各种周期积分的正则化。应用包括一般线性群的张量积l函数理论的推广，GL（n，F）的可区分残差自同构表示的刻画，酉群或元群积上的Gross-Prasad型一般自同构表示的周期不灭的必要条件。此外，我们刻画了外立方l函数具有极点的GL(6)的倒态自同构表示，并发展了一般线性群的对称方形l函数的Rankin-Selberg积分表示理论，并用关于一般线性群双盖的例外表示的周期积分来刻画其极点。

I gave a necessary and sufficient condition for the nonvanishing of theta liftings. I constructed regularization of various period integrals of automorphic forms. Applications include a generalization of the theory of tensor product L-functions for general linear groups, a characterization of GL(n,F)-distinguished residual automorphic representations of GL(n,E), necessary conditions for non-vanishing of periods of Gross-Prasad type of generic automorphic representations on products of unitary groups or metaplectic groups.Moreover, we characterize cuspidal automorphic representations of GL(6) whose exterior cube L-functions have a pole and develop a theory of a Rankin-Selberg integral representation representing the symmetric square L-function for general linear groups and characterize its pole in terms of period integrals with respect to exceptional representations of the double cover of general linear groups.