Second Moment of Central Values of Half-Integral Weight Modular Forms and Subconvexity

Steven Creech, Henry Twiss, Zhining Wei +1

We let $f$ be a half-integral weight modular form of weight $\kappa >4$ on ${\Gamma }_0(4)$ that is an eigenfunction of all Hecke operators $T_n$, so that $T_{n}f={\Lambda }_f(n)n^{\frac{\kappa -1}{2}}f$. Let…