{"paper":{"title":"Hamiltonian for the zeros of the Riemann zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.NT"],"primary_cat":"quant-ph","authors_text":"Carl M. Bender, Dorje C. Brody, Markus P. M\\\"uller","submitted_at":"2016-08-12T05:08:32Z","abstract_excerpt":"A Hamiltonian operator $\\hat H$ 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 $\\hat H$ is $2xp$, which is consistent with the Berry-Keating conjecture. While $\\hat H$ is not Hermitian in the conventional sense, ${\\rm i}{\\hat H}$ is ${\\cal PT}$ symmetric with a broken ${\\cal PT}$ symmetry, thus allowing for the possibility that all eigenvalues of $\\hat H$ are real. A heuristic analysis is presented for the construction of the m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03679","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}