{"paper":{"title":"Asymptotics of signed Bernoulli convolutions scaled by multinacci numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DS"],"primary_cat":"math.CA","authors_text":"Tian-You Hu, Xianghong Chen","submitted_at":"2017-10-04T19:44:03Z","abstract_excerpt":"We study the signed Bernoulli convolution $$\\nu_\\beta^{(n)}=*_{j=1}^n \\left (\\frac12\\delta_{\\beta^{-j}}-\\frac12\\delta_{-\\beta^{-j}}\\right ),\\ n\\ge 1$$ where $\\beta>1$ satisfies $$\\beta^m=\\beta^{m-1}+\\cdots+\\beta+1$$ for some integer $m\\ge 2$. When $m$ is odd, we show that the variation $|\\nu_\\beta^{(n)}|$ coincides the unsigned Bernoulli convolution $$\\mu_\\beta^{(n)}=*_{j=1}^n \\left (\\frac12\\delta_{\\beta^{-j}}+\\frac12\\delta_{-\\beta^{-j}}\\right ).$$ When $m$ is even, we obtain the exact asymptotic of the total variation $\\|\\nu_\\beta^{(n)}\\|$ as $n\\rightarrow\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01780","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":""},"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"}