7 problems

Let $\chi\pmod{q}$ be a Dirichlet character, and write $s=\sigma+it$. Generalized Lindelöf hypothesis. For every $\varepsilon>0$, if $\sigma\geq 1/2$ and $|s-1|\geq 1/2$, then … Th…

For real $x$ and $t>1$, let $S_{\left\lfloor x/n^t\right\rfloor,x}$ denote the set considered in the paper, with the function defining $S_{f,x}$ taken to be non-piecewise. Sparsity…

For $T\ge 3$, let $\mathcal{L}(T)$ and $\beta=\beta(T)$ be non-decreasing continuous functions satisfying … Let $W=W(x)$ be increasing with $W(x)\gg(\log x)^A$ for a sufficiently l…

Modified prime number theorem.

For a fixed modulus $c$, define … where $\Lambda(n)$ is the von Mangoldt function and $\phi(c)$ is Euler's totient function. Hooley's conjecture. … Hooley did not specify the size…

Friedlander–Granville conjecture. For every fixed $\varepsilon>0$,

Maximal oscillation conjecture. As $x\to\infty$,