{"paper":{"title":"On the dimension of the graph of the classical Weierstrass function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DS","authors_text":"Bal\\'azs B\\'ar\\'any, Julia Romanowska, Krzysztof Bara\\'nski","submitted_at":"2013-09-15T13:42:00Z","abstract_excerpt":"This paper examines dimension of the graph of the famous Weierstrass non-differentiable function \\[ W_{\\lambda, b} (x) = \\sum_{n=0}^{\\infty}\\lambda^n\\cos(2\\pi b^n x) \\] for an integer $b \\ge 2$ and $1/b < \\lambda < 1$. We prove that for every $b$ there exists (explicitly given) $\\lambda_b \\in (1/b, 1)$ such that the Hausdorff dimension of the graph of $W_{\\lambda, b}$ is equal to $D = 2+\\frac{\\log\\lambda}{\\log b}$ for every $\\lambda\\in(\\lambda_b,1)$. We also show that the dimension is equal to $D$ for almost every $\\lambda$ on some larger interval. This partially solves a well-known thirty-yea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3759","kind":"arxiv","version":5},"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"}