论文标题
正式的希尔伯特·帕利亚（Hilbert-Pólya）猜测
Formally Self-Adjoint Hamiltonian for the Hilbert-Pólya Conjecture
论文作者
论文摘要
我们构建了一种正式的自我拥护者哈密顿式，其特征值对应于Riemann Zeta函数的非平凡零。我们考虑了一个二维的哈密顿量，它通过单一的转换将浆果烤的哈密顿量与半线的数字操作员结合在一起。我们证明，由挤压（扩张）操作员和数量运算符的指数组成的单一操作员将哈密顿量的特征功能限制在一个维度上，因为挤压参数趋向于无限。 Riemann Zeta函数出现在生成的狭窄波函数的边界上，并且由于施加的边界条件而消失。如果可以使此处提出的形式论证更加严格，尤其是如果可以严格证明哈密顿人在强加的边界条件下保持自立性，那么我们的方法有可能暗示Riemann假设是正确的。
We construct a formally self-adjoint Hamiltonian whose eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. We consider a two-dimensional Hamiltonian which couples the Berry-Keating Hamiltonian to the number operator on the half-line via a unitary transformation. We demonstrate that the unitary operator, which is composed of squeeze (dilation) operators and an exponential of the number operator, confines the eigenfunction of the Hamiltonian to one dimension as the squeezing parameter tends towards infinity. The Riemann zeta function appears at the boundary of the resulting confined wave function and vanishes as a result of the imposed boundary condition. If the formal argument presented here can be made more rigorous, particularly if it can be shown rigorously that the Hamiltonian remains self-adjoint under the imposed boundary condition, then our approach has the potential to imply that the Riemann hypothesis is true.
