Subconvexity for Symmetric Square L-functions off-centre

Abstract

Let $p$ be a prime. Let $f$ be a holomorphic modular form of level $p$ with trivial nebentypus. We prove the bound $L\left({\text{sym}}^{2}f,\frac{1}{2}+it\right){\ll }_{f,\epsilon }{p}^{1/2+\epsilon }{t}^{3/4-1/12+\epsilon }$. This bound is subconvex in the $t$-aspect and almost convex in the level aspect simultaneously.

First Draft. Comments welcome