Eigenvalue Density, Li’s Positivity, and the Critical Strip
He, Y., Jejjala, V. & Minic, D. (2009). Eigenvalue Density, Li’s Positivity, and the Critical Strip (VPI-IPNAS-09-03). Blacksburg, USA: Virgina Tech, IPNAS.
Abstract
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.
| Publication Type: | Report |
|---|---|
| Additional Information: | archiveprefix: arXiv primaryclass: math-ph |
| Subjects: | Q Science > QC Physics |
| Departments: | School of Science & Technology > Mathematics |
| Related URLs: |
Metadata
MetadataActions (login required)
Admin Login