4 problems

For $m\geq 1$, let … with $\mathbf{k}=(k,k)$ and $\overline{\alpha}=(\alpha_1,\alpha_2)$ satisfying $\alpha_j\ll\log T$ and $\alpha_1-\alpha_2\ll 1$. Chandee's conjecture. The foll…

Let $q$ tend to infinity through primes, let $Y$ be the shift-height parameter, and let $R$ be a piecewise smooth positively oriented path encircling $0$ and $-s$. Dirichlet shifte…

Let $k\in\mathbb N$, let $Y=Y(T)$, and let $R$ be a piecewise smooth positively oriented path encircling $0$ and $-s$. Shifted moments conjecture. For $T\geq1$, … This holds for…

Let $\zeta(s)$ be the Riemann zeta function. For $M\geq 1$ and real numbers $\mu_1,\ldots,\mu_M,\nu_1,\ldots,\nu_M$, define $W_M$ by … where $\mathcal{S}_{2M}'$ consists of permuta…