We prove strong hybrid subconvex bounds simultaneously in the q and t aspects for L-functions of selfdual \({{\,\textrm{GL}\,}}_3\) cusp forms twisted by primitive Dirichlet characters. We additionally prove analogous hybrid subconvex bounds for central values of certain \({{\,\textrm{GL}\,}}_3 \times {{\,\textrm{GL}\,}}_2\) 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 \({{\,\textrm{GL}\,}}_3\) 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 \({{\,\textrm{GL}\,}}_3 \times {{\,\textrm{GL}\,}}_2 \leftrightsquigarrow \leftrightsquigarrow {{\,\textrm{GL}\,}}_4 \times {{\,\textrm{GL}\,}}_1\) spectral reciprocity formula, which relates a \({{\,\textrm{GL}\,}}_2\) moment of \({{\,\textrm{GL}\,}}_3 \times {{\,\textrm{GL}\,}}_2\) Rankin–Selberg L-functions to a \({{\,\textrm{GL}\,}}_1\) moment of \({{\,\textrm{GL}\,}}_4 \times {{\,\textrm{GL}\,}}_1\) Rankin–Selberg L-functions. A key additional input is a Lindelöf-on-average upper bound for the second moment of Dirichlet L-functions restricted to a coset, which is of independent interest.
