{"paper":{"title":"Disjointness of the M\\\"obius Transformation and M\\\"obius Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"el Houcein el Abdalaoui, Igor E. Shparlinski","submitted_at":"2017-11-29T19:13:34Z","abstract_excerpt":"We study the distribution of the sequence of elements of the discrete dynamical system generated by the M\\\"obius transformation $x \\mapsto (ax + b)/(cx + d)$ over a finite field of $p$ elements. Motivated by a recent conjecture of P. Sarnak, we obtain nontrivial estimates of exponential sums with such sequences that imply that trajectories of this dynamical system are disjoined with the M\\\"obius function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11062","kind":"arxiv","version":3},"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"}