8 problems

Generalized Riemann Hypothesis. The non-trivial zeros of $L(s,f)$ all lie on the critical line

Let $N(\sigma,T)$ denote the number of nontrivial zeros $\rho=\beta+i\gamma$ of the Riemann zeta-function with $\beta\ge\sigma$ and $|\gamma|\le T$. Density Hypothesis. For all…

Density hypothesis.

Montgomery-style mean value conjecture. The displayed estimate should hold for all such sequences, coefficients, and parameters. The conjecture proposes a stronger mean value theor…

Stronger density hypothesis. For every $\varepsilon>0$, there exists $\delta=\delta(\varepsilon)\in(0,1)$ such that, for every $\nu\in[0,1/2-\varepsilon)$ and $T\geq1$,

For $0\leq\sigma\leq1$ and $T\geq1$, let $N(\sigma,T,\chi)$ denote the number of zeros $\rho=\beta+i\gamma$ of $L(s,\chi)$, counted with multiplicity, satisfying…

Let $N(\sigma,T)$ denote the number of zeros $\rho=\beta+i\gamma$ of the Riemann zeta-function with $\beta\geq\sigma$ and $0<\gamma\leq T$. Selberg's zero-density conjecture. For a…

Let $\mathcal{L}$ belong to the subclass $\mathcal{S}'$ of the Selberg class, and let $N_\mathcal{L}(\sigma,T)$ denote the number of zeros…