t-Aspect Subconvexity Bound for $GL(2)$ L-functions

Let $f $ be a holomorphic Hecke eigenforms or a Hecke-Maass cusp form for the full modular group $ SL(2, mathbb{Z})$. In this paper we shall use circle method to prove the Weyl exponent for $GL(2)$ $L$-functions. We shall prove that [ L left( frac{1}{2} + it right) ll_{f, epsilon} left( 1 + |t|right)^{1/3 + epsilon}, ] for any $epsilon > 0.$