Strong hybrid subconvexity for twisted selfdual GL₃ L-functions

We prove strong hybrid subconvex bounds simultaneously in the q and t aspects for L -functions of selfdual \,GL\,₃ GL 3 cusp forms twisted by primitive Dirichlet characters. We additionally prove analogous hybrid subconvex bounds for central values of certain \,GL\,₃ × \,GL\,₂ GL 3 × GL 2 Rankin–Selberg L -functions. The subconvex bounds that we obtain are strong in the sense that, modulo current knowledge on estimates for the second moment of \,GL\,₃ GL 3 L -functions, they are the natural limit of the first moment method pioneered by Li and by Blomer. The method of proof relies on an explicit \,GL\,₃ × \,GL\,₂ \,GL\,₄ × \,GL\,₁ GL 3 × GL 2 ↭ ↭ GL 4 × GL 1 spectral reciprocity formula, which relates a \,GL\,₂ GL 2 moment of \,GL\,₃ × \,GL\,₂ GL 3 × GL 2 Rankin–Selberg L -functions to a \,GL\,₁ GL 1 moment of \,GL\,₄ × \,GL\,₁ GL 4 × GL 1