{"paper":{"title":"Proof of the Gawron-Miska-Ulas conjecture concerning unboundedness of coefficients of power series expansion of $\\prod_{n=0}^{\\infty}(1-x^{2^{n}})^m$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jinmin Yu, Shaofang Hong, Wenzhong Lei","submitted_at":"2026-06-24T13:44:27Z","abstract_excerpt":"It is well known that $F(x)=\\prod_{n=0}^{\\infty}(1-x^{2^n})$ is the generating function of the Prouhet-Thue-Morse sequence $\\{(-1)^{\\sigma_2(n)}\\}_{n=0}^\\infty$, where $\\sigma_2(n)$ is the sum of (binary) digits of $n$. Let $m$ be an integer. In 2018, Gawron, Miska and Ulas initiated the study of arithmetic properties of power series expansion of the function $$F_m(x)=F(x)^m=\\sum_{n=0}^{\\infty}t_m(n) x^n,$$ and proposed a conjecture stating that for any given integer $m\\ge 2$, the sequence $\\{t_m(n)\\}_{n=0}^{\\infty}$ is unbounded. In this paper, we introduce a new method to investigate this co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25825","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/2606.25825/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"}