On the Physics of the Riemann Zeros

2010/04/07 by Yang-Hui He, He, Yang-Hui, Vishnu Jejjala +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Number Theory (math.NT) #hep-th #math-ph #math.MP #math.NT

paper · pdf · doi:10.48550/arxiv.1004.1172

8 pages, LaTeX, Quantum Theory and Symmetries 6 conference proceedings

arxiv created 2010/04/07 · arxiv updated 2010/04/12

Abstract

We discuss a formal derivation of an integral expression for the Li coefficients associated with the Riemann xi-function which, in particular, indicates 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 discuss a physical interpretation of this result within the Hilbert-Polya approach. In this context we also outline a relation between string theory and the Riemann Hypothesis.

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