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

Authors

  • Yang-Hui He London Institute, Royal Institution; City, University of London; & University of Oxford
  • Vishnu Jejjala
  • Djordje Minic

Keywords:

Zero-counting formula, Riemann zeta function, Li coefficients

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.

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Published

2022-07-15

How to Cite

(1)
He, Y.-H.; Jejjala, V.; Minic, D. Eigenvalue Density, Li’s Positivity, and the Critical Strip. inSTEMM 2022, 1, 1-14.