$t$-aspect subconvexity for $GL(2)$ $L$-functions

Abstract

Let $f$ be a holomorphic cusp form for $S{L}_2(\mathbb{Z})$ of weight $k>1$. In these notes, we follow Munshi to prove the Burgess bound $$L(1/2+it,f){\ll }_{f,\epsilon }(1+|t|{)}^{1/2-1/8+\epsilon }.$$

Typos corrected, and a mistake taken care of in section 5. The result is unchanged