Overviews on Berry-Keating conjecture, Hilbert-P\'{o}lya conjecture and Riemann hypothesis

Newly motivated by the G-dynamics as a part of the quantum covariant Hamiltonian system (QCHS), we try to use it to untangle the complex affairs of the three closely related conjectures: Riemann hypothesis (RH), Berry-Keating conjecture (BKC) and Hilbert-P\'{o}lya conjecture (HPC). Truly, a suitable solution $\zeta \left( 1/2+\sqrt{-1}{{w}^{\left( q \right)}} \right)=0$ holds for RH, it means that such an unbounded self-adjoint operator indeed exists, and it's the G-dynamics $\hat{w}^{(cl)}$ as a strong candidate for such self-adjoint operator which described the geometric frequency, exactly.

本研究受作为量子协变哈密顿系统（quantum covariant Hamiltonian system, QCHS）组成部分的G动力学（G-dynamics）启发，尝试借助该框架厘清三大紧密相关猜想的复杂关联问题：黎曼猜想（Riemann hypothesis, RH）、贝里-基廷猜想（Berry-Keating conjecture, BKC）与希尔伯特-波利亚猜想（Hilbert-Pólya conjecture, HPC）。确切而言，满足黎曼猜想的恰当解为$zetaleft(1/2 + sqrt{-1}w^{(q)}
ight)=0$，这意味着此类无界自伴算子（unbounded self-adjoint operator）确实存在；而该G动力学$hat{w}^{(cl)}$正是描述几何频率的此类自伴算子的强力候选者。