5 problems

Let $\mathcal{F}(K)=\{L_k(s):1\le k\le K\}$, let $M=\log K$, let $f$ be the test function, and let $W_f$, $S_\zeta$, $S_L$, $S_{A'}$, and $S_\Gamma$ be the integrals defined in the…

Let $\mathcal{F}(K)=\{L_k(s):1\le k\le K\}$, let $M=\log K$, and let $R_K(\alpha,\gamma)$ be the ratios-conjecture prediction built from the Euler product $G(\alpha,\gamma)$. For s…

Let $f$ be an even Schwartz function, let $w$ be the weight function, and define the weighted ratio average … For $\operatorname{Re}(2\nu'+\nu)>-1$ and…

The biquadratic-curve one-level density conjecture. As $g\to\infty$,

Let $\phi(x)$ be a Schwartz-class function on $\mathbb{R}$ whose Fourier transform has compact support. Define … For $f\in H_k$, let $\Lambda(s,f)$ be its completed $L$-function, a…