{"paper":{"title":"A Variation Norm Carleson Theorem Along the Primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Anastasios Fragkos, Ben Krause, Nazar Miheisi, Yu-Chen Sun","submitted_at":"2026-07-06T18:57:36Z","abstract_excerpt":"Let $\\Lambda$ denote the von Mangoldt function; we prove that for each $r > 2$, there exist constants \\[ r' < \\mathbf{c}(r) < 2 < \\mathbf{C}(r), \\qquad \\lim_{r \\to \\infty} \\mathbf{c}(r) = 1, \\ \\lim_{r \\to \\infty} \\mathbf{C}(r) = \\infty \\] so that the discrete variational Carleson operator along the primes \\begin{align} \\mathcal{V}^r \\Big( \\sum_{n \\neq 0} f(x-n) \\Lambda(|n|) \\frac{e^{2\\pi i \\lambda n}}{n} : \\lambda \\in \\mathbb{T} \\Big) \\end{align} is bounded on $\\ell^p$ for all $\\mathbf{c}(r) < p < \\mathbf{C}(r)$, while the variation is unbounded when $p \\leq r'$. At the non-variational endpoin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05560","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/2607.05560/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"}