{"paper":{"title":"Order and Chaos in some Trigonometric Series: Curious Adventures of a Statistical Mechanic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Michael K.-H. Kiessling","submitted_at":"2012-06-21T23:10:18Z","abstract_excerpt":"This paper tells the story how a MAPLE-assisted quest for an interesting undergraduate problem in trigonometric series led some \"amateurs\" to the discovery that the one-parameter family of deterministic trigonometric series $\\pzcS_p: t\\mapsto \\sum_{n\\in\\Nset}\\sin(n^{-{p}}t)$, $p>1$, exhibits both order and apparent chaos, and how this has prompted some professionals to offer their expert insights. It is proved that $\\pzcS_p(t) = \\alpha_p\\rm{sign}(t)|t|^{1/{p}}+O(|t|^{1/{(p+1)}})\\;\\forall\\;t\\in\\Rset$, with explicitly computed constant $\\alpha_p$. Experts' commentaries are reproduced stating the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5031","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"}