Moments of Derivatives of Modular L-Functions

Abstract

Abstract Let f be a newform for the group $\Gamma_{0}(q)$ and χd be a primitive quadratic character of conductor $|d|$. In this article, we prove an asymptotic for the second moment of the derivative of $L(s,\, f \otimes \chi_{8d})$ at the central point $1/2$, which was previously known under grand Riemann hypothesis (GRH) by Petrow [9].