{"paper":{"title":"Pair correlation of sequences $(\\lbrace a_n \\alpha \\rbrace)_{n \\in \\mathbb{N}}$ with maximal order of additive energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gerhard Larcher, Wolfgang Stockinger","submitted_at":"2018-02-07T11:58:18Z","abstract_excerpt":"We show for sequences $\\left(a_{n}\\right)_{n \\in \\mathbb{N}}$ of distinct positive integers with maximal order of additive energy, that the sequence $\\left(\\left\\{a_{n} \\alpha\\right\\}\\right)_{n \\in \\mathbb{N}}$ does not have Poissonian pair correlations for any $\\alpha$. This result essentially sharpens a result obtained by J. Bourgain on this topic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02901","kind":"arxiv","version":2},"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"}