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For a fixed cusp form $\pi$ on $\operatorname{GL}_3(\mathbb{Z})$ and avarying Dirichlet character $\chi$ of prime conductor $q$, we prove that thesubconvex bound \[ L(\pi \otimes \chi, \tfrac{1}{2}) \ll q^{3/4 - \delta} \]holds for any $\delta < 1/36$. This improves upon the earlier bounds $\delta <1/1612$ and $\delta < 1/308$ obtained by Munshi using his $\operatorname{GL}_2$variant of the $\delta$-method. The method developed here is more direct. Wefirst express $\chi$ as the degenerate zero-frequency contribution of acarefully chosen summation formula \`a la Poisson. After an elementary"amplification" step exploiting the multiplicativity of $\chi$, we then apply asequence of standard manipulations (reciprocity, Voronoi, Cauchy--Schwarz andthe Weil bound) to bound the contributions of the nonzero frequencies and ofthe dual side of that formula.

Subconvex bounds on GL(3) via degeneration to frequency zero