Further Comments on Realization of Riemann Hypothesis via Coupling Constant Spectrum

Realization of the Riemann Hypothesis via Coupling Constant Spectrum

We present a Non-relativistic Quantum mechanical model, which exhibits the realization of Riemann Conjecture. The technique depends on exposing the $S$-wave Jost function at zero energy and in identifying it with the Riemann $ξ(s)$ function following a seminal paper of N. N. Khuri.

On recent strategies proposed for proving the Riemann hypothesis

We comment on some apparently weak points in the novel strategies recently developed by various authors aiming at a proof of the Riemann hypothesis. After noting the existence of relevant previous papers where similar tools have been used, we refine some of these strategies. It is not clear at the moment if the problems we point out here can be resolved rigorously, and thus a proof of the RH be obtained, along the lines proposed. However, a specific suggestion of a procedure to overcome the encountered difficulties is made, what constitutes a step towards this goal.

（1+1）维Rindler时空中黎曼假设的马约拉纳相对论量子谱方法

A Majorana Relativistic Quantum Spectral Approach to the Riemann Hypothesis in (1+1)-Dimensional Rindler Spacetimes

本文提出一种受希尔伯特-波利亚启发的谱方法，在（1+1）维Rindler时空中构造马约拉纳粒子的厄米哈密顿量，使其能量本征值谱与黎曼zeta函数非平凡零点一一对应，并结合本质自伴性与非交换几何论证所有零点均位于临界线上，从而为证明黎曼假设提供新路径。