Subconvexity for symmetric square $L$-functions

Abstract

Let $f$ be a holomorphic modular form of prime level $p$ and trivial nebentypus. We show that there exists a computable $\delta >0$, such that $$L\left(\frac{1}{2},{\mathrm{Sym}}^{2}f\right)\ll p^{\frac{1}{2}-\delta },$$ with the implied constant depending only on $\delta$ and the weight of $f$.

rough preliminary draft of the manuscript