4 problems

Consider the family of quadratic Dirichlet $L$-functions $L(s,\chi_d)$, where $\chi_d$ is a quadratic Dirichlet character, and let $g_k$ denote the constant in the corresponding co…

Let $\zeta(z)$ denote the Riemann zeta function, and let $U Sp(2N)$ denote the compact symplectic symmetry group in dimension $2N$. Keating–Snaith symplectic symmetry conjecture. T…

Let $A=\{\alpha_1,\ldots,\alpha_K\}$ and $B=\{\gamma_1,\ldots,\gamma_Q\}$ be sets of complex shifts satisfying the restrictions stated in the source. Let $\mathbb{H}_{2g+1}$ be the…

CFKRS conjecture. If $|\operatorname{Re}(s)-\frac12|\ll1/\log X$ for all $s\in S$, then as $X\to\infty$,