{"paper":{"title":"Multifractal Analysis of generalized Thue-Morse trigonometric polynomials","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aihua Fan, J\\\"org Schmeling, Weixiao Shen","submitted_at":"2022-12-26T17:42:13Z","abstract_excerpt":"We consider the generalized Thue-Morse sequences $(t_n^{(c)})_{n\\ge 0}$ ($c \\in [0,1)$ being a parameter) defined by $t_n^{(c)} = e^{2\\pi i c s_2(n)}$, where $s_2(n)$ is the sum of digits of the binary expansion of $n$. For the polynomials $\\sigma_{N}^{(c)} (x) := \\sum_{n=0}^{N-1} t_n^{(c)} e^{2\\pi i n x}$, we have proved in [18] that the uniform norm $\\|\\sigma_N^{(c)}\\|_\\infty$ behaves like $N^{\\gamma(c)}$ and the best exponent $\\gamma(c)$ is computed. In this paper, we study the pointwise behavior and give a complete multifractal analysis of the limit $\\lim_{n\\to\\infty}n^{-1}\\log |\\sigma_{2^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.13234","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.13234/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}