{"paper":{"title":"Precise Asymptotics and Exact Formulas for Tensor Product Energies of Fibonacci Lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.MG","math.NA"],"primary_cat":"math.NT","authors_text":"Melia Haase, Nicolas Nagel","submitted_at":"2026-05-20T08:35:43Z","abstract_excerpt":"We consider the asymptotics of sums of the form $$ \\frac1{F_n^\\sigma} \\sum_{m = 1}^{F_n-1} \\frac{f(m/F_n)}{\\left|{\\sin(\\pi m/F_n)}\\right|^\\sigma} \\frac{f(F_{n-1}m/F_n)}{\\left|{\\sin(\\pi F_{n-1}m/F_n)}\\right|^\\sigma} $$ where $(F_n)_{n \\in \\mathbb N} = (1, 1, 2, 3, 5, 8, 13, \\dots)$ are the Fibonacci numbers. Such sums appear, for example, in the context of discrepancy theory and numerical integration methods reformulated as energy minimization problems.\n  We show that for parameters $\\sigma > 1$ and a large class of functions $f$ the above sum behaves asymptotically like $$ C n + D + O\\left((1-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20895","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/2605.20895/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"}