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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 $$ C n + D + O\\left((1-"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.20895","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-20T08:35:43Z","cross_cats_sorted":["cs.NA","math.MG","math.NA"],"title_canon_sha256":"4ee828741f6f5e17d13f25e59fd1ea989cf5dcf1f526fcaedfc29abe68d3e34c","abstract_canon_sha256":"7c023baf9401d345747af6092e3ef9602cfa150386b9ffc1236424fd530d1e7b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:26.861110Z","signature_b64":"qu2D1wylK3K6DphJDz/hxwJtI/Jw0qR7qFrIO+2oXBhfnTaY1lfklrg2mLZQ8qRTGrLmQbTU2Uv6T/JhpoXiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44dcc03eb44409861638ea457a2b1049d9af2926a43436db81f1a7f31a394b7e","last_reissued_at":"2026-05-21T01:05:26.860381Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:26.860381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Precise Asymptotics and Exact Formulas for Tensor Product Energies of Fibonacci Lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.MG","math.NA"],"primary_cat":"math.NT","authors_text":"Melia Haase, Nicolas Nagel","submitted_at":"2026-05-20T08:35:43Z","abstract_excerpt":"We consider the asymptotics of sums of the form $$ \\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. 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