{"paper":{"title":"On the Hardy--Littlewood majorant problem for arithmetic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Bartosz Trojan, Ben Krause, Mariusz Mirek","submitted_at":"2015-05-03T09:28:13Z","abstract_excerpt":"The aim of this paper is to exhibit a wide class of sparse deterministic sets, $\\mathbf B \\subseteq \\mathbb{N}$, so that\n  \\[ \\limsup_{N \\to \\infty} N^{-1}|\\mathbf B \\cap [1,N]|= 0, \\]\n  for which the Hardy--Littlewood majorant property holds:\n  \\[ \\sup_{|a_n|\\le 1} \\Big\\| \\sum_{n\\in\\mathbf B\\cap[1, N]} a_n e^{2 \\pi i n \\xi}\\Big \\|_{L^p(\\mathbb{T}, {\\mathrm d} \\xi)} \\leq \\mathbf{C}_p \\Big\\| \\sum_{n\\in\\mathbf B\\cap[1, N]} e^{2 \\pi i n \\xi} \\Big\\|_{L^p(\\mathbb{T},\n  {\\mathrm d} \\xi)}, \\] where $p \\geq p_{\\mathbf{B}}$ is sufficiently large, the implicit constant $\\mathbf{C}_p$ is independent of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00409","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":""},"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"}