SUBCONVEXITY BOUND FOR GL(2) L‐FUNCTIONS: T ‐ASPECT

Let f be a holomorphic or Hecke–Maass cusp form for the full modular group SL ( 2 , Z ) . In this paper we use the circle method to prove a Weyl‐type subconvexity for GL ( 2 )L ‐functions. We prove that L 1 2 + i t , f ≪ f , ε1 + | t | 1 / 3 + ε , for any ε > 0 .