Moments of Derivatives of Modular L-Functions

Let f be a newform for the group Γ₀(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 ⊗ χ8d) at the central point $1/2$, which was previously known under grand Riemann hypothesis (GRH) by Petrow [9].