7 problems

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

Let $F$ and $G$ be primitive functions in the Selberg class, let $t(m;F)$ denote the ordinates of the non-trivial zeros of $F$, and define … where $w(u)=4/(4+u^2)$. Murty–Perelli c…

Let $\gamma,\gamma',\gamma”$ range over ordinates of nontrivial zeros of the Riemann zeta function, put $\widetilde\gamma=(\log T)/(2\pi)\,\gamma$, and let $\hat r$ be the relevant…

Assume that every non-trivial zero of every function in the Selberg class has real part $1/2$. For a Selberg-class function $F$, let $\mathcal{F}(X,T;F)$ be its zero-correlation st…

Assume that every non-trivial zero of every function in the Selberg class has real part $1/2$. For a function $F$ in the Selberg class, let $t(m;F)$ denote the ordinates of its non…

Assume the Riemann hypothesis, and write the non-trivial zeros of the Riemann zeta function as $1/2+i\gamma(m)$. Let $d^{\mathrm{mean}}(t)=(2\pi)^{-1}\log(|t|/(2\pi))$, let…

For a primitive Dirichlet character $\chi$ modulo $k$, let $L(s,\chi)$ be its Dirichlet $L$-function, and let the non-trivial zeros on the critical line be written as…