Short second moment bound and Subconvexity for GL(3) $L$-functions

Abstract

Let $\ddot{I}€$ be a Hecke cusp form for ${\mathrm{SL}}_3(\mathbb{Z})$. We bound the second moment average of $L(s,\ddot{I}€)$ over a short interval to obtain the subconvexity estimate $$L(1/2+it,\ddot{I}€){\ll }_{\ddot{I}€,\epsilon }(1+|t|{)}^{3/4-1/8+\epsilon }.$$

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