Moments of derivatives of modular $L$-functions

Abstract

Let $f$ be an Hecke eigenform for the group $\hat{I}{“}_0(q)$ and $\ddot{I}{‡}_d$ be a primitive quadratic character of conductor $|d|$. In this article, we prove an asymptotic for the second moment of the derivative of $L(s,f\otimes \ddot{I}{‡}_{8d})$ at the central point $1/2$, which was previously known under GRH by Petrow \cite{petrow}.

19 Pages