6 problems

Let $\zeta(s)=\sum_{n=1}^{\infty}n^{-s}$ be the Riemann zeta-function, and let $t$ be real. The notation $f(t)\ll g(t)$ means that $|f(t)|\leq Cg(t)$ for some constant $C$ in the r…

Exponent-pair conjecture. The pair

Let $M_{Dir}$ be the matrix associated with Dirichlet polynomials, and let $M_{Dir}M_{Dir}^*$ be its Gram matrix. Off-diagonal square-root conjecture. Every off-diagonal entry of…

Let $\mathcal{N}$ be an admissible sequence of positive real numbers, and let $\mathrm{LH}(\mathcal{N})$ denote the Lindelöf hypothesis for that sequence. Gonek–Graham–Lee conjectu…

Let $\mathcal{N}$ be an admissible sequence of positive integers, and let $\mathrm{LH}(\mathcal{N})$ denote the Lindelöf hypothesis for that sequence. Gonek–Graham–Lee conjecture.…

Let $e_q(x)=e^{2\pi i x/q}$, let $\overline{m}$ denote the multiplicative inverse of $m$ modulo $q$, and let $\mathfrak{a}\in\{0,1\}$. For $y>0$, define … where $\int_{(b)}$ denote…