A Hamiltonian operator H[over ^] is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. The classical limit of H[over ^] is 2xp, which is consistent with the Berry-Keating conjecture. While H[over ^] is not Hermitian in the conventional sense, iH[over ^] is PT symmetric with a broken PT symmetry, thus allowing for the possibility that all eigenvalues of H[over ^] are real. A heuristic analysis is presented for the construction of the metric operator to define an inner-product space, on which the Hamiltonian is Hermitian. If the analysis presented here can be made rigorous to show that H[over ^] is manifestly self-adjoint, then this implies that the Riemann hypothesis holds true.
This research output has an Altmetric Attention Score of 339. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 07 October 2026.
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#123,036
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Outputs from Physical Review Letters
#173
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#2,367
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Outputs of similar age from Physical Review Letters
#3
of 555 outputs
Altmetric has tracked 34,545,128 research outputs across all sources so far. Compared to these this one has done particularly well and is in the 99th percentile: it's in the top 5% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 51,661 research outputs from this source. They typically receive a lot more attention than average, with a mean Attention Score of 13.9. This one has done particularly well, scoring higher than 99% of its peers.
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We're also able to compare this research output to 555 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 99% of its contemporaries.
