2 problems

Let $f$ be a holomorphic cusp form with associated quadratic-twist family $\mathcal{F}_f^{+}(X)$, and let $R_f(\alpha,\gamma)$ denote the average of the ratio of shifted $L$-functi…

Let $f_d$ be a quadratic twist in the family and define … where $s=1/2+it$. For $-1/4<\operatorname{Re}(\alpha),\operatorname{Re}(\beta)<1/4$,…