{"paper":{"title":"Automatic sequences are orthogonal to aperiodic multiplicative functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Clemens M\\\"ullner, Mariusz Lema\\'nczyk","submitted_at":"2018-11-01T19:09:28Z","abstract_excerpt":"Given a finite alphabet $\\mathbb{A}$ and a primitive substitution $\\theta:\\mathbb{A}\\to\\mathbb{A}^\\lambda$ (of constant length $\\lambda$), let $(X_\\theta,S)$ denote the corresponding dynamical system, where $X_{\\theta}$ is the closure of the orbit via the left shift $S$ of a fixed point of the natural extension of $\\theta$ to a self-map of $\\mathbb{A}^{\\mathbb{Z}}$. The main result of the paper is that all continuous observables in $X_{\\theta}$ are orthogonal to any bounded, aperiodic, multiplicative function $\\mathbf{u}:\\mathbb{N}\\to\\mathbb{C}$, i.e. \\[ \\lim_{N\\to\\infty}\\frac1N\\sum_{n\\leq N}f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00594","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"}