Short second moment bound and Subconvexity for GL(3) $L$-functions (2206.06517v2)

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 $$ L(1/2+it, \pi) \ll{\pi, \varepsilon} (1+|t|)^{3/4-1/8+\varepsilon}. $$