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DC Field | Value | Language |
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dc.contributor.author | Brody, DC | - |
dc.contributor.author | Bender, CM | - |
dc.contributor.author | Müller, MP | - |
dc.date.accessioned | 2017-03-08T12:48:40Z | - |
dc.date.available | 2017-03-08T12:48:40Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Physical Review Letters, (2017) | en_US |
dc.identifier.issn | 0031-9007 | - |
dc.identifier.uri | http://bura.brunel.ac.uk/handle/2438/14197 | - |
dc.description.abstract | A Hamiltonian operator ^H 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 is 2xp, which is consistent with the Berry- Keating conjecture. While ^H is not Hermitian in the conventional sense, i ^H is PT symmetric with a broken PT symmetry, thus allowing for the possibility that all eigenvalues of ^H are real. A heuristic analysis is presented for the construction of the metric operator to de ne an inner-product space, on which the Hamiltonian is Hermitian. If the analysis presented here can be made rigorous to show that ^H is manifestly self-adjoint, then this implies that the Riemann hypothesis holds true. | en_US |
dc.language.iso | en | en_US |
dc.publisher | American Physical Society | en_US |
dc.title | Hamiltonian for the zeros of the Riemann zeta function | en_US |
dc.type | Article | en_US |
dc.relation.isPartOf | Physical Review Letters | - |
pubs.publication-status | Accepted | - |
Appears in Collections: | Dept of Mathematics Research Papers |
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FullText.pdf | 155.76 kB | Adobe PDF | View/Open |
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