Abstract
The Riemann hypothesis 1,2 states that the complex zeros of ζ(s) lie on the critical line Re s=1/2; that is, the nonimaginary solutions E n of (1) are all real. Here we will present some evidence that the E n are energy levels, that is eigenvalues of a hermitian quantum operator (the ‘Riemann operator’), associated with the classical hamiltonian (2) where x is the (one-dimensional) position coordinate and p the conjugate momentum. This is frankly speculative, because large gaps remain that are not merely technical.
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Berry, M.V., Keating, J.P. (1999). H=xp and the Riemann Zeros. In: Lerner, I.V., Keating, J.P., Khmelnitskii, D.E. (eds) Supersymmetry and Trace Formulae. NATO ASI Series, vol 370. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4875-1_19
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DOI: https://doi.org/10.1007/978-1-4615-4875-1_19
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