He, Y., Jejjala, V. & Minic, D. (2009). Eigenvalue Density, Li’s Positivity, and the Critical Strip (Report No. VPI-IPNAS-09-03). Blacksburg, USA: Virgina Tech, IPNAS.
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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.
|Additional Information:||archiveprefix: arXiv primaryclass: math-ph|
|Subjects:||Q Science > QC Physics|
|Divisions:||School of Engineering & Mathematical Sciences > Department of Mathematical Science|
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