{"paper":{"title":"Fast and slow points of Birkhoff sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fr\\'ed\\'eric Bayart (LMBP), Yanick Heurteaux (LMBP), Zoltan Buczolich (ELTE)","submitted_at":"2019-01-11T08:22:05Z","abstract_excerpt":"We investigate the growth rate of the Birkhoff sums $S_{n,\\alpha} f(x)=\\sum_{k=0}^{n-1} f(x+k\\alpha)$, where $f$ is a continuous function with zero mean defined on the unit circle $\\mathbb T$ and $(\\alpha,x)$ is a \"typical\" element of $\\mathbb T^2$. The answer depends on the meaning given to the word \"typical\". Part of the work will be done in a more general context."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03504","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"}