Abstract
We discuss a formal derivation of an integral expression for the Li coefficients associated with the Riemann ξ-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-Pólya approach. In this context we also outline a relation between string theory and the Riemann Hypothesis.
Highlights
Riemann Zeros and the Li CriterionThis talk is devoted to the physics of the non-trivial zeros of the Riemann ξ function, the so-called Riemann zeros [1]
The profound proofs of the Riemann Hypothesis for the case of finite fields by Weil, Deligne and others are essentially geometric, and one might expect a deeply geometric resolution of the Riemann Hypothesis [12]. Motivated by this expectation in this concluding section we present a possibly exciting connection between Gromov-Witten (GW) invariants, topological string theory and the Riemann zeros [2]
: (1), we know that the Lagarias bound on σ1(n) in terms of the harmonic numbers is equivalent to Riemann Hypothesis and (2), we know of examples of Gromov-Witten invariants which are equal to σ1(n)
Summary
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