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

He, Y., Jejjala, V. and Minic, D. (2009). Eigenvalue Density, Li’s Positivity, and the Critical Strip (Report No. 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 Mathematics, Computer Science & Engineering > Mathematics
Related URLs:
URI: http://openaccess.city.ac.uk/id/eprint/884
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