Strong hybrid subconvexity for twisted selfdual $${\text {GL}}_3$$ L-functions

Abstract We prove strong hybrid subconvex bounds simultaneously in the q and t aspects for L -functions of selfdual $${{\,\textrm{GL}\,}}_3$$ GL 3 cusp forms twisted by primitive Dirichlet characters. We additionally prove analogous hybrid subconvex bounds for central values of certain $${{\,\textrm{GL}\,}}_3 \times {{\,\textrm{GL}\,}}_2$$ 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 $${{\,\textrm{GL}\,}}_3$$ 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 $${{\,\textrm{GL}\,}}_3 \times {{\,\textrm{GL}\,}}_2 \leftrightsquigarrow \leftrightsquigarrow {{\,\textrm{GL}\,}}_4 \times {{\,\textrm{GL}\,}}_1$$ GL 3 × GL 2 ↭ ↭ GL 4 × GL 1 spectral reciprocity formula, which relates a $${{\,\textrm{GL}\,}}_2$$ GL 2 moment of $${{\,\textrm{GL}\,}}_3 \times {{\,\textrm{GL}\,}}_2$$ GL 3 × GL 2 Rankin–Selberg L -functions to a $${{\,\textrm{GL}\,}}_1$$ GL 1 moment of $${{\,\textrm{GL}\,}}_4 \times {{\,\textrm{GL}\,}}_1$$ GL 4 × GL 1