{"paper":{"title":"On Minima of Difference of Epstein Zeta Functions and Exact Solutions to Lennard-Jones Lattice Energy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Senping Luo","submitted_at":"2022-12-21T02:46:30Z","abstract_excerpt":"Let $\\zeta(s,z)=\\sum_{(m,n)\\in\\mathbb{Z}^2\\backslash\\{0\\}}\\frac{(\\Im(z))^s}{|mz+n|^{2s}}$ be the Eisenstein series/Epstein Zeta function. Motivated by widely used Lennard-Jones potential\n  \\begin{equation}\\aligned\\nonumber \\mathcal{V}(|\\cdot|^2):=4\\varepsilon\\Big( (\\frac{\\sigma}{|\\cdot|})^{12}-(\\frac{\\sigma}{|\\cdot|})^{6} \\Big), \\endaligned\\end{equation}\n  in physics, in this paper, we consider the following lattice minimization problem \\begin{equation}\\aligned\\nonumber \\min_{z\\in\\mathbb{H}}\\Big(\\zeta(6,z)-b\\zeta(3,z)\\Big), \\;\\;b=\\frac{1}{\\sigma^6} \\endaligned\\end{equation}\n  and completely cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.10727","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.10727/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}