{"paper":{"title":"Additive Energy and Irregularities of Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CO"],"primary_cat":"math.NT","authors_text":"Christoph Aistleitner, Gerhard Larcher","submitted_at":"2016-08-24T14:45:58Z","abstract_excerpt":"We consider strictly increasing sequences $\\left(a_{n}\\right)_{n \\geq 1}$ of integers and sequences of fractional parts $\\left(\\left\\{a_{n} \\alpha\\right\\}\\right)_{n \\geq 1}$ where $\\alpha \\in \\mathbb{R}$. We show that a small additive energy of $\\left(a_{n}\\right)_{n \\geq 1}$ implies that for almost all $\\alpha$ the sequence $\\left(\\left\\{a_{n} \\alpha\\right\\}\\right)_{n \\geq 1}$ has large discrepancy. We prove a general result, provide various examples, and show that the converse assertion is not necessarily true."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06847","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"}