The circle method and bounds for $L$-functions - III: $t$-aspect subconvexity for GL(3) $L$-functions

Abstract

Let $\pi$ be a Hecke-Maass cusp form for $SL(3,\mathbb Z)$. In this paper we will prove the following subconvex bound $$ L(\tfrac{1}{2}+it,\pi)\ll_{\pi,\varepsilon} (1+|t|)^{3/4-1/16+\varepsilon}. $$