Eigenvalue Density, Li’s Positivity, and the Critical Strip

We rewrite the zero-counting formula within the critical strip of the Riemann zeta function as a cumulative density distribution; this subsequently allows us to derive an integral expression for the Li coefficients associated with the Riemann ξ-function and, in particular, indicate that their positivity criterion is obeyed, whereby entailing the criticality of the non-trivial zeros. We also offer a physical interpretation of the result and discuss the Hilbert–Pólya approach. ∗[email protected] †[email protected] ‡[email protected]