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

Preprint, Other ORP type English OPEN
He, Yang-Hui ; Jejjala, Vishnu ; Minic, Djordje (2009)
  • Publisher: Virgina Tech, IPNAS
  • Subject: QC | Mathematical Physics | High Energy Physics - Theory | Mathematics - Number Theory

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 formally derive an integral expression for the Li coefficients associated with the Riemann xi-function which, in particular, indicate that their positivity criterion is obeyed, whereby entailing the criticality of the non-trivial zeros. We conjecture the validity of this and related expressions without the need for the Riemann Hypothesis and also offer a physical interpretation of the result and discuss the Hilbert-Polya approach.
Share - Bookmark