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Let $f$ be a holomorphic cusp form for $SL_2(\mathbb{Z})$ of weight $k>1$. Inthese notes, we follow Munshi to prove the Burgess bound $$L(1/2+it,f)\ll_{f,\varepsilon} (1+|t|)^{1/2-1/8+\varepsilon}. $$

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