A new subconvex bound for $\mathrm{GL}(3)$ $L$-functions in the $t$-aspect

Abstract

We revisit Munshi's proof of the $t$-aspect subconvex bound for $\mathrm{GL}(3)$ $L$-functions, and we are able to remove the `conductor lowering' trick. This simplification along with a more careful stationary phase analysis allows us to improve Munshi's bound to, $$L(1/2+it,\ddot{I}€){\ll }_{\ddot{I}€,\hat{I}\mu }(1+|t|{)}^{3/4-3/40+\hat{I}\mu }.$$

19 pages; Corrected errors and made revisions to the stationary phase analysis