Strong Subconvexity for Self-Dual GL(3) L-Functions

In this paper, we prove strong subconvexity bounds for self-dual GL(3)\ L-functions in the t-aspect and for GL(3)× GL(2)L$-functions in the $GL(2)$-spectral aspect. The bounds are strong in the sense that they are the natural limit of the moment method pioneered by Xiaoqing Li, modulo current knowledge on estimate for the second moment of $GL(3)L-functions on the critical line.