9 problems

The Riemann zeta function is defined by $[... ELLIPSIZATION...$ and continued meromorphically to the complex plane. For complex shifts $[... ELLIPSIZATION...$, define the $2k$-poin…

Let $Z_F$ be constructed from the non-trivial zeta zeros, and consider orderings of those zeros, including the standard ordering by increasing imaginary part. Canonical Ordering co…

Let $Z_F$ be the fractal zero set constructed from the positive imaginary parts of the non-trivial zeros of $\zeta(s)$ by the recursive four-subinterval construction described in t…

Let $P_{\text{ess}}$ be the essential fractal prime set, with information measure $\iota(P_{\text{ess}})=-\zeta(1/2)$, and let $Z_F$ be the fractal zero set constructed from the po…

Chandee's conjecture. One has

Let $T>1$, let $\tau$ be chosen uniformly from $[T,2T]$, and let $0<\alpha<1$ with $\theta\sim(\log\log T)^{-\alpha}$. Consider an interval of size … The smoothing-scale conjecture…

Local ratios conjecture. For these fixed parameters,

Let $\zeta(s)$ be the Riemann zeta function, and consider the positive imaginary parts of its nontrivial zeros. The zeta linear-independence conjecture. These imaginary parts are l…

Let $B$ denote the Bernoulli operator, defined formally by $e^{-Bx}=\frac{x}{e^x-1}$, and let $\xi$ be the Riemann xi function. The expression $\sin \pi B\cdot\xi(B+s)$ is defined…