Short second moment bound and Subconvexity for GL(3) $L$-functions
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abstract
Let $pi$ be a Hecke cusp form for $mathrm{SL}_3(mathbb{Z})$. We bound the second moment average of $L(s,pi)$ over a short interval to obtain the subconvexity estimate $$ L(1/2+it, pi) ll_{pi, varepsilon} (1+|t|)^{3/4-1/8+varepsilon}. $$
