Yao-Ming Shi

Construction of Finite Hilbert--P\'olya Matrices from Weil's Explicit Formula

Starting from the Riemann--$\Xi$ specialization of Weil's explicit formula, we construct finite real-symmetric Prime--Weil matrices $(\mathbf S)$ from pole, archimedean, and finite prime-power data. This construction is a finite-dimensional arithmetic model within the Hilbert--P\'olya program, which seeks a self-adjoin...